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Medical images make up for more than 25% of global attacks on privacy. Securing them is therefore of utmost importance. Chaos based image encryption is one of the most method suggested in the literature for image security due to their intrinsic characteristic, including ergodicity, aperiodicity, high sensitivity to initials conditions and system parameters. Dynamic systems such as bridge circuit, jerk circuit, Van der Pol circuit, Colpitts oscillator and many other pseudo-random numbers generators have been used in the process of encrypting images. Among them, are the jerk oscillators that have been used with different nonlinearities. In this paper, a new, simple, off-shell component of jerk oscillator (jerk quintic) with an interesting nonlinear function is proposed. Its dynamical behaviors are investigated using classical tools like bifurcation diagrams, Maximum Lyapunov exponent plot, basin of attraction, phase portraits. We showed that the nonlinear function is responsible of complex nonlinear behaviors displayed by the novel circuit, including symmetric/asymmetric bifurcation and coexisting bubbles, multistability just to name a few. The real implementation of the interesting circuit is embedded in a microcontroller verifies these dynamics. As an application of this contribution in multimedia, an encryption algorithm built on a new confusion-diffusion architecture using pseudo random number generated in high chaoticity regime of the new circuit is proposed. The cryptosystem underwent thorough security tests and proved to be fast thanks to the 3D map used, given its complex dynamical behaviors and large chaotic area. This approach yields a robust cipher that underwent thorough security tests better than the one in the literature like average NPCR=99.61, UACI=33.48, key space-sensitivity, entropy=7.9994, average correlation=0.0040. Furthermore, it proved to be robust in terms of noise and data loss in the transmission channel, offering a large key space of 10180 and an entropy close to the standard value, thus rendering the cryptosystem robust against various attacks, especially brute force and exhaustive attacks. [ABSTRACT FROM AUTHOR]

We investigate spatiotemporal pattern formation in cancer growth using discrete time and space variables. We first introduce the coupled map lattices (CMLs) model and provide a dynamical analysis of its fixed points along with stability results. We then offer parameter criteria for flip, Neimark–Sacker, and Turing bifurcations. In the presence of spatial diffusion, we find that stable homogeneous solutions can experience Turing instability under certain conditions. Numerical simulations reveal a variety of spatiotemporal patterns, including patches, spirals, and numerous other regular and irregular patterns. Compared to previous literature, our discrete model captures more complex and richer nonlinear dynamical behaviors, providing new insights into the formation of complex patterns in spatially extended discrete tumor models. These findings demonstrate the model's ability to capture complex dynamics and offer valuable insights for understanding and treating cancer growth, highlighting its potential applications in biomedical research. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new tritrophic food chain model. We address the conditions for the coexistence of two different zooplankton species and one phytoplankton species. The results of the numerical and analytical studies of the model show that the most relevant parameters influencing the plankton ecosystem, to maintain a stable coexistence equilibrium, are the: carrying capacity and the constant intrinsic growth rate of the phytoplankton population, and the conversion rate with a mortality rate of carnivorous zooplankton. We prove the existence and direction of Hopf bifurcation in non delay system. To account for the time delay in the conversion of herbivorous consumption to carnivorous zooplankton, we incorporate a discrete delay into the consume response function. Furthermore, we establish some adequate conditions to prove the occurrence of Hopf bifurcation induced by delay in the delayed model. We also plot two-parameter bifurcation diagrams. The numerical results support the analytical findings. [ABSTRACT FROM AUTHOR]

Studying the magnetoelastic coupling vibration of moving plates under the influence of complex air-gap magnetic fields is of theoretical significance for modeling multi-field dynamics and solving nonlinear dynamic issues. This paper considers the scenario where an armature wall acts on one side of an axially moving ferromagnetic thin plate and investigates the multiple resonance of the plate subjected to a harmonic excitation in the air-gap magnetic field. First, based on electromagnetic theory combined with boundary conditions of the magnetic field, the distribution of the air-gap magnetic field is determined by solving the Laplace equation of the magnetic scalar potential function. Next, expressions for the magnetic and Lorentz forces acting on the moving ferromagnetic plate are derived. Then, the thin plate energy expression considering geometric nonlinearity and the virtual work expressions of the forces are obtained by applying the Kirchhoff plate theory and the principle of virtual work. Subsequently, the nonlinear vibration equation of the system with magnetoelastic coupling is established using the Hamiltonian variational principle. Utilizing the established mechanical model, the principal-internal resonance is analytically solved employing the Galerkin and multiple scales methods, with stability criteria for steady-state motion solutions determined using Lyapunov stability theory. Finally, the nonlinear dynamics of the system are analyzed through analytical and numerical examples, and the influences of different physical parameter variations on the dynamic behavior are discussed. Results indicate that variations in physical parameters affect the amplitude, resonance region, and regions of multiple solutions of the system. Moreover, the system may transition to chaos through quasiperiodic torus breakdown or period-doubling bifurcation due to changes in physical parameters. The results of this study provide theoretical references for research in magnetoelastic coupling nonlinear dynamics in fields of magnetic drive and electromagnetic control, as well as for product design and optimization. [ABSTRACT FROM AUTHOR]

This work investigates the global dynamics of the bottom hole assembly with non-uniformly distributed cutters on drill-bit which improves stability of steady drilling. In this work, the drill string with a bottom hole assembly is considered as a lumped parameter model in the axial and torsional directions to accommodate axial and torsional vibrations, respectively. The regenerative effect due to the variation in the depth of cut is considered the only source of instability in the system. The engagement of individual cutters with the cut surface is modeled by formulating separate cut surface profile between two simultaneous cutters which is essential in capturing the true global dynamics of the system. Linear stability analysis through eigenvalue analysis reveals the system's improved stability compared to the system equipped with uniformly distributed cutters. An optimal distribution of cutters on the drill-bit for different number of cutters leading to the most stable steady drilling is obtained. This optimal distribution has been found to be robust with respect to changes in the rock strength as well as drill-rig parameters. A detailed nonlinear numerical analysis of the system with the optimal distribution reveals the existence of subcritical and supercritical Hopf bifurcation at different lobes of stability boundaries. Further analysis unveils various complex phenomenon, such as the co-existence of the steady solutions with the chaotic solution, partial bit-bounce, complete bit-bounce, and stick–slip vibrations. [ABSTRACT FROM AUTHOR]

The use of plastic is very widespread in the world and the spread of plastic waste has also reached the oceans. Observing marine debris is a serious threat to the management system of this pollution. Because it takes years to recycle the current wastes, while their amount increases every day. The importance of mathematical models for plastic waste management is that it provides a framework for understanding the dynamics of this waste in the ocean and helps to identify effective strategies for its management. A mathematical model consisting of three compartments plastic waste, marine debris, and recycle is studied in the form of a system of ordinary differential equations. After describing the formulation of the model, some properties of the model are given. Then the equilibria of the model and the basic reproduction number are obtained by the next generation matrix method. In addition, the global stability of the model are proved at the equilibria. The bifurcations of the model and sensitivity analysis are also used for better understanding of the dynamics of the model. Finally, the numerical simulations of discussed models are given and the model is examined in several aspects. It is proven that the solutions of the system are positive if initial values are positive. It is shown that there are two equilibria E 0 and E ∗ and if B R < 1 , it is proven that E 0 is globally stable, while when B R > 1 , the equilibrium E ∗ exists and it is globally stable. Also, at B R = 1 the model exhibits a forward bifurcation. The sensitivity analysis of B R concludes that the rates of waste to marine, new waste, and the recycle rate have most effect on the amount of marine debris. [ABSTRACT FROM AUTHOR]

Parental care is a behavioral strategy observed in many living organisms, where parents devote time and resources to ensuring their offspring's survival, growth, and well-being. Such care can be in various forms and involve different levels of investment, depending on the species and its ecological context. This study examines how parental care among prey contributes to the coexistence of prey and predator in an ecosystem. For this, we proposed a three-dimensional prey-predator system with the following factors–(i) stage structure and parental care in prey population, (ii) linear functional response for the interaction between immature prey and predators, whereas Holling type II functional response for the case of mature prey. We examined the conditions for the existence of equilibrium points, and their local and global stability for our proposed model. We observed the switching of stability of equilibria via transcritical bifurcation concerning the maturation rate and attack rate on adult prey. We examined all three possible existence scenarios for the maturation rate, e.g., extinction of both populations, prey-only existence, and coexistence of both prey and predator. We also investigated the appearance and disappearance of the limit cycle via Hopf-bifurcation concerning the predation rate and saturation constant of adult prey. We observed that parental care has a stabilizing effect on the system dynamics. Numerical simulations and graphical representations have been done to verify our theoretical findings. Sensitivity analysis is conducted to illustrate the importance of parental care in a stage-structure model. With the introduction of parental care parameter in prey species, we observe a more realistic dynamics of stage structured model. [ABSTRACT FROM AUTHOR]

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In this paper we study the stability of a Killing cylinder in hyperbolic 3-space when regarded as a capillary surface for the partitioning problem. In contrast with the Euclidean case, we consider a variety of totally umbilical support surfaces, including horospheres, totally geodesic planes, equidistant surfaces and round spheres. In all of them, we explicitly compute the Morse index of the corresponding eigenvalue problem for the Jacobi operator. We also address the stability of compact pieces of Killing cylinders with Dirichlet boundary conditions when the boundary is formed by two fixed circles, exhibiting an analogous to the Plateau–Rayleigh instability criterion for Killing cylinders in the Euclidean space. Finally, we prove that the Delaunay surfaces can be obtained by bifurcating Killing cylinders supported on geodesic planes. [ABSTRACT FROM AUTHOR]

In 1959 Crawford S. Holling formulated a classification to model the action of the predators over their prey, doing empirical works. In this taxonomy, he introduced only three types of functional responses dependent only on the prey population, which are described by saturated functions. Later, various other types have been proposed, including the functional responses dependent on both populations. This work concerns the study of the Leslie–Gower type predator-prey model, incorporating the Rosenzweig functional response described by a power law. The elected function does not conform to the types proposed by Holling since it is unbounded, being, besides, non-differentiable for x = 0 ; nonetheless, the obtained system is Lipschitzian. Moreover, the existence of a separatrix curve Σ in the phase plane is proven, which is divided into two complementary sectors. According to the position of the initial conditions with respect to the curve, the trajectories can have different ω -limit sets, which can be the equilibrium 0 , 0 , or a positive equilibrium, or a heteroclinic curve, or a stable limit cycle. These properties show the great difference of this model with the original Leslie–Gower model, in which a unique positive equilibrium exists, which is globally asymptotically stable, when it exists. Then, the analyzed system has a richer dynamic than the original system in which a linear functional response is considered, also unbounded. Numerical simulations and bifurcation diagrams are given to endorse our analytical results. [ABSTRACT FROM AUTHOR]

The bifurcations and monotonicity of the period function of the Lakshmanan–Porsezian–Daniel equation with Kerr law of nonlinearity are discussed. Firstly, by the traveling wave transformations, the Lakshmanan–Porsezian–Daniel equation is reduced to the planar Hamiltonian system whose Hamiltonian function includes a 6-th degree polynomial. Then we give the phase portraits of the Hamiltonian system, and some traveling waves including dark wave solutions, kink and anti-kink solutions and periodic solutions are constructed by using the bifurcation method of dynamical systems. Furthermore, we discuss the monotonicity of the period function of periodic wave solutions by using some Lemmas proposed by Yang and Zeng (Bull Sci Math 133(6):555-557, 2009). Finally, some numerical simulations are presented. [ABSTRACT FROM AUTHOR]

A nonlinear parabolic equation with transformation of the spatial variable and periodic conditions on the circle is considered. Using the method of separation of variables, we obtain properties of eigenfunctions and eigenvalues of the corresponding linearized problem. Using the method of central manifolds, we prove the existence and stability of spatially inhomogeneous stationary solutions. Based on the Galerkin method, we analyze approximate solutions of the original problem. [ABSTRACT FROM AUTHOR]

This study explores the dynamics of sequentially arranged coupled oscillator loops, focusing on inducing steadily rotating phase waves. Notably, when interconnected loops of differing sizes are analyzed, the resulting phase waves exhibit a synchronization pattern, either in-phase or out-of-phase, with pulse counts proportional to their size ratios. This synchronization is further investigated through the introduction of subharmonic injection locking, achieved by applying an external frequency signal matching one of the pulses within the rotating phase waves. Our research delineates the core characteristics of phase waves across oscillator loops of varying sizes, offering a novel approach to generate multiple rotary pulses and amplify the subharmonic response by fine-tuning the oscillators' bias voltage. This paper sheds light on the underlying mechanisms of phase wave synchronization and subharmonic injection locking, with potential applications in enhancing the functionality of coupled oscillator systems. [ABSTRACT FROM AUTHOR]

We propose a Neurosimilator, novel analog neuron circuit and mathematical model of its dynamics that both simulate with high precision the spiking behavior of known types of excitable cells. The analog circuit is compact and can be built using off-the-shelf components. This could facilitate its use in teaching neuroscience and biophysics. The circuit is scalable down to the pF-valued capacitors, presenting an advantage in research on the analog nerve fiber networks. The equations of circuit dynamics contain exponential non-linearities and Heaviside functions, so that the model combines features from the generalized adapting exponential integrate-and-fire neuron model and from the intermittent feedback Hindmarsh-Rose model, but it is not directly related to them. Our four-dimensional system (4D-Neurosimilator) simulates most of excitable cells' spiking, bursting and chaotic behavior depending on only fewer predefined parameters. In bursting and chaotic oscillatory patterns, the model demonstrates self-adaptive energy flow redistribution. The energy expenditure amounts to ≈36 µJ per one spiking event in original model and to ≈0.63 pJ in its down-scaled version. The model has computational cost comparable to that of the Hodgkin–Huxley model, but it tends to handle noisy input stimulations more efficiently. Our work provides novel insights to the simulation of neuron's non-linear dynamics and may constitute another choice of available model in computational neuroscience research that expands the limits of a tradeoff between accuracy, biological explainability, noise-resistance and computing time. [ABSTRACT FROM AUTHOR]

We study bifurcations of nonlinear waves (spatially inhomogeneous solutions) emerging from homogeneous equilibrium states of an initial boundary value problem, arising in nonlinear optics, for a nonlinear parabolic equation on a disk with a spatial argument rescaling operator and with time delay. In the plane of the main parameters of the equation, we construct stability (instability) domains of homogeneous equilibrium states and study the dynamics of the stability domains depending on the rescaling coefficient. We investigate the mechanisms of stability loss by homogeneous equilibrium states, the possible bifurcations of spatially inhomogeneous self-oscillatory solutions, and their stability. We demonstrate the possibility of bifurcation of stable rotational and spiral waves. [ABSTRACT FROM AUTHOR]

We study the dynamics of a system of differential equations with the diffusion interaction and an additional internal coupling. Such systems are interesting because a slight variation in the coefficient at the additional coupling allows obtaining intricate scenarios of phase rearrangements. For the system under study, we find the critical dependence of the parameters such that zero equilibrium loses stability as two spatially inhomogeneous states appear in one case and a cycle in another case. With the parameter values close to the critical ones, asymptotic formulas are obtained for the regimes that branch off from the zero solution. [ABSTRACT FROM AUTHOR]

In this paper, a predator–prey model with fear-induced group defense and Monod–Haldane functional response is considered. We establish a connection between fear effect and group defense by incorporating anti-predator sensitivity and emphasizing their impact on the dynamics of the model. Our analysis shows that increasing anti-predator sensitivity lowers the threshold for initiating group defense, leading to faster adoption of prey defense strategies. The preliminary results include positivity, boundedness, and persistence. We find that under certain thresholds, anti-predator sensitivity can sustain species persistence; otherwise, predators may face extinction. Changes in anti-predator sensitivity significantly influence system dynamics, notably affecting the quantity and stability of equilibrium points. We provide a comprehensive analysis of the global properties of both boundary and interior equilibrium points. Additionally, the system undergoes Transcritical, Saddle-node and Hopf bifurcation by considering the anti-predator sensitivity as a bifurcation parameter and Bogdanov–Takens bifurcation with respect to the prey birth rate and the anti-predator sensitivity. Numerical simulations support our theoretical findings. Our study highlights the complex interplay of fear effect, group defense, and anti-predator sensitivity in predator–prey dynamics. These results may provide valuable biological insights into predator–prey interactions. [ABSTRACT FROM AUTHOR]

Our paper presents the chaotic behaviour of atmospheric systems with fractional order by using Bernoulli wavelet collocation technique. This technique has not yet been implemented on this model. The study have analysed the dynamics of three climate components—green house gases, temperature and permafrost thaw. To determine the simplicity and efficiency of the developed technique, numerical results have obtained. The combination of graphs and tables shows the stability and efficacy of the developed strategy. Based on the obtained results, we have draw the conclusion that this method offers superior accuracy and efficiency to other methods such as Adam Bashforth's method, Forward Euler's method and fde 12 solver method. This study have reveals the effectiveness of the numerical technique as well as the effect of the non integer derivative on atmospheric models. All calculations have been done using a mathematical program called Matlab. Environmental science can be better understood through these studies. [ABSTRACT FROM AUTHOR]

This study aims to thoroughly investigate the dynamics of a predator–prey model with a Beddington-De Angelis functional response. We assume that the prey refuge is proportional to both species. We establish the standard properties of boundedness, permanence, and local stability. We show that under certain parameter conditions, transcritical bifurcation and Hopf bifurcation occur. To understand the nature of the limit cycle, we determine the direction of the Hopf bifurcation. We focus on the significant ranges of the predators' prey capturing rate and examine how the level of prey fear and the predator's mutual interference affect the system's stability. Through numerical analysis, we study the behavior of the Lyapunov exponent and observe multiple self-repeating shrimp-shaped patterns that indicate periodic attractors in discrete-time predator–prey system. These structures appear across a broad region associated with chaotic dynamics. Additionally, if the intensity of white noise is kept below a specific threshold, the deterministic control approach is equally effective in environmental fluctuation. Numerical simulations support these findings. [ABSTRACT FROM AUTHOR]

Memristor has been extensively employed to emulate neuron/synapse-inspired behaviors and to characterize the electromagnetic induction generated by ionic flowing. A link between memristive features and neural electrical activities is significantly necessary to be investigated. Thus, we propose a new neuron model with a locally active threshold flux-controlled (LTF) memristor, which depicts the electromagnetic induction. The LTF memristive neuron model can exhibit a regular evolution and transition of various firing patterns dependent upon the negative different conductance of the memristor, through performing the corresponding numerical simulations. It is demonstrated that due to the locally active threshold effect, the obtained model has complex firing behaviors. The memristive neural network is connected via chemical synapses. The memristive neural network under the modulation of excitatory and inhibitory chemical synapses shows different synchronous patterns. The captured results reveal that the locally active threshold effect is crucial for the generation of complex firing modes and the emergence of synchronization behaviors. [ABSTRACT FROM AUTHOR]

The carrying capacity's functional dependence illustrates the reality that any species' activities can enhance or diminish its carrying capacity. Migration is the need of many species to achieve better opportunities for survival. In a tri-trophic system, the middle predator often immigrates to consume its prey and often emigrates to secure themselves from predators. This work deals with formulating and investigating a mathematical model reflecting the aforementioned ecological aspects. We perform a detailed analysis to prove the boundedness of the solutions. Further, we examine the existence and stability of equilibrium points, followed by the bifurcation analysis. We explore various global and local bifurcations like Hopf, saddle-node, transcritical, and homoclinic for the critical parameters β (measuring the impact of prey activities on the carrying capacity) and k 1 (measuring the migration rate of a predator). Higher values of β generate unpredictability, which helps explain the enrichment paradox. The presence of a chaotic attractor and bi-stability of node-node type is demonstrated via numerical simulation. The migratory behavior of middle predators can control chaos in the system. Furthermore, we study the proposed model in the presence of seasonal fluctuations. Persistence of the non-autonomous system, existence, and global stability of periodic solutions are analyzed theoretically. The seasonality in β brings the bi-stability between chaotic and periodic attractors, and seasonality in growth rate of the prey causes bi-stability between 2-periodic and 4-periodic attractors. Moreover, the bi-stability in the autonomous system shifts to the global stability of an equilibrium in the seasonal model due to the seasonality in β . When birth and death rates are seasonal along with β , the extinction of one or more populations is possible. The non-autonomous system also exhibits bursting oscillations when seasonality is present in the death rate. Our findings reveal that the population's intense constructive and destructive actions can allow the basal prey to thrive while eradicating both predators. [ABSTRACT FROM AUTHOR]

The security performance of image encryption schemes based on chaotic systems has been greatly improved. Specifically, those chaotic systems with high-dimension or special attractors have shown more benefits for enhancing performance. By introducing the tangent function, a 4-dimensional chaotic system with infinite coexisting attractors is constructed. And the dynamical behaviors are analyzed through phase diagrams, bifurcation diagrams, Lyapunov exponent spectrum and spectral entropy complexity diagram. The results demonstrate that the system exhibits self-replication with respect to the initial value y0 and possesses rich dynamical properties, such as infinite coexisting attractors, sensitivity to initial values and period-doubling bifurcation. These characteristics make it suitable for chaotic cryptography applications. Subsequently, a lossless double color image encryption scheme is designed based on the constructed system. The scheme adopts a diffusion-scrambling-diffusion processing method, and cleverly utilizes the information of the original plaintext image in the scrambling process, which significantly enhances the ability to resist known plaintext attacks or selected plaintext attacks. The experimental results verify that the designed algorithm not only effectively encrypts color and grayscale images, but also allows for encryption images of any size. Moreover, the algorithm implementation process is efficient and ensures high security performance, effectively resisting differential attacks, rotation attacks and cropping attacks. This research exploration on the chaotic characteristics of the nonlinear high-dimensional system and its application in image encryption is expected to provide theoretical guidance in the field of secure communication. [ABSTRACT FROM AUTHOR]

In this manuscript, an attempt is made to investigate the natural convection process in hybrid nanofluid (Al2O3–Cu/water) contained in an isosceles triangular porous conduit with heated side/congruent walls by considering the performance of various thermal conditions. The bottom side of the enclosure is kept isothermally cooled, whereas uniformly and non-uniformly thermal boundary conditions are applied on congruent/side walls. Thermophysical properties of water and nanoparticles are used to model the problem with the help of continuity, momentum, and energy equations. Appropriate combination of variables is used to make the transport equations dimensionless. The obtained partial differential equations (PDEs) have been solved numerically by using Galerkin-based finite element method (GFEM). Trends of Darcy number Da (10 - 5 ≤ Da ≤ 10 - 3) , Rayleigh number Ra (10 3 ≤ Ra ≤ 10 6) , and solid volume fractions ϕ 1 , ϕ 2 (0.00 ≤ ϕ 1 , ϕ 2 ≤ 0.06) on streamlines, local Nusselt number, and isotherms have been presented in pictorial form. Bifurcation analysis is also described to make the contribution more versatile. Finally, results obtained from present simulation are matched for limited version (i.e., ϕ 1 = ϕ 2 = 0.0 ) in order to ensure the accuracy of the GFEM and modeling procedure of the mathematical model. [ABSTRACT FROM AUTHOR]

We continue studies of the nonlocal erosion equation that is used as a mathematical model of the formation of a spatially inhomogeneous relief on semiconductor surfaces. We show that such a relief can form as a result of local bifurcations in the case where the stability of the spatially homogeneous equilibrium state changes. We consider a periodic boundary-value problem and study its codimension- bifurcations. For solutions describing an inhomogeneous relief, we obtain asymptotic formulas and study their stability. The analysis of the mathematical problem is based on modern methods of the theory of dynamical systems with an infinite-dimensional phase space, in particular, on the method of integral manifolds and on the theory of normal forms. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of practically susceptible population, which is a fraction of the biologically susceptible population. Assuming that the fraction depends on the severity of the epidemic and the public's level of precaution (as a response of the public to the epidemic), we propose a general framework model with the response level evolving with the epidemic. We firstly verify the well-posedness and confirm the disease's eventual vanishing for the framework model under the assumption that the basic reproduction number R 0 < 1 . For R 0 > 1 , we study how the behavioural response evolves with epidemics and how such an evolution impacts the disease dynamics. More specifically, when the precaution level is taken to be the instantaneous best response function in literature, we show that the endemic dynamic is convergence to the endemic equilibrium; while when the precaution level is the delayed best response, the endemic dynamic can be either convergence to the endemic equilibrium, or convergence to a positive periodic solution. Our derivation offers a justification/explanation for the best response used in some literature. By replacing "adopting the best response" with "adapting toward the best response", we also explore the adaptive long-term dynamics. [ABSTRACT FROM AUTHOR]

Granular materials belong to the class of complex materials within which rich properties can emerge on large scales despite a simple physics operating on the microscopic scale. Most notable is the dissipative behaviour of such materials mainly through non-linear frictional interactions between the grains which go out of equilibrium. A whole variety of intriguing features thus emerges in the form of bifurcation modes in either patterning or un-jamming. This complexity of granular materials is mainly due to the geometrical disorder that exists in the granular structure. Diverse configurations of grain collections confer to the assembly the capacity to deform and adapt itself against different loading conditions. Whereas the incidence of frictional properties in the macroscopic plastic behavior has been well described for long, the role of topological reorganizations that occur remains much more elusive. This paper attempts to shed a new light on this issue by developing ideas following the configurational entropy concept within a proper statistical framework. As such, it is shown that contact opening and closing mechanisms can give rise to a so-called configurational dissipation which can explain the irreversible topological evolutions that granular materials undergo in the absence of frictional interactions. [ABSTRACT FROM AUTHOR]

In this article, a spatial epidemic model with media coverage is studied. By both mathematical analysis and numerical simulation, we found that there are some typical dynamics of population density such as the formation of the hole, stripe, spot, coexistence of hole and stripe or spot and stripe. The obtained results exhibit that parameters describing media coverage have a significant influence on the spatial pattern of the disease. More specifically, the sequential change in behaviour of the spatial pattern is observed as the parameter that accounts for media coverage increases. These changes analogous to the effect due to the rise in the basic reproduction number. The results presented in this article thus can be applied to any particular disease with some modification to study the effects of media coverage on disease dynamics. The model is although simple but the idea can be well extended to other complex problems. [ABSTRACT FROM AUTHOR]

This study presents an initial study on the bifurcation analysis of bistable oscillator dynamics for human hair-cell bundle structures. The hair-cell bundles within the human cochlea possess highly nonlinear stiffness while sound transmission. To better understand this bistable oscillator dynamics, this study focused on the bifurcation phenomena using the Floquet theory. To define the bifurcations associated with super- and sub-harmonic resonances, the harmonic balance method (HBM) was first utilized with Hill's method, for determining the dynamics stability conditions. In addition, the Floquet multipliers were mapped to examine their relationship with the bifurcation characteristics. To examine the bifurcation characteristics, only the Floquet multipliers associated with unstable conditions were selected because those associated with stable conditions were decaying terms. Then, the complex values of the Floquet multipliers at specific frequency locations were compared with the bifurcations' characteristics. When numerically calculated bifurcations were compared with the results obtained using the HBM, mapping the Floquet multipliers was sufficient for predicting the bifurcations of a biomimetic system inspired by the hair-cell bundle structure. This study suggests practical techniques for employing the HBM with Hill's method by mapping the Floquet multipliers to investigate complex nonlinearities that occur in bistable-stiffness systems. [ABSTRACT FROM AUTHOR]

In this work, we propose and study a two species Lotka–Volterra competition model, where the first species experiences the mate-finding Allee effect caused by the second species. First, we study the presence and stability of all conceivable positive equilibria and boundary equilibria of this system. Next, by utilizing the Sotomayor theorem, we demonstrate that, given appropriate parameter circumstances, both a saddle-node bifurcation and a transcritical bifurcation exist. Finally, numerical simulations were carried out to validate our theoretical results further. We found that under certain conditions, the system appears to be bistable when the trait-mediated indirect effect is low. However, when the trait-mediated indirect effect is too high, the bistability of the system disappears, and the first species eventually tends to extinction. [ABSTRACT FROM AUTHOR]

In this paper, we consider two-dimensional periodic capillary-gravity waves traveling under the influence of a vertical electric field. The full system is a nonlinear, two-layered, free boundary problem. The interface dynamics are derived by coupling Euler equations for the velocity field of the fluid with voltage potential equations governing the electric field. We first introduce the naive flattening technique to transform the free boundary problem into a fixed boundary problem. We then prove the existence of small-amplitude electrohydrodynamic waves with constant vorticity using local bifurcation theory. Moreover, we show that these electrohydrodynamic waves are formally stable in the linearized sense. Furthermore, we obtain a secondary bifurcation curve that emerges from the primary branch, consisting of ripple solutions on the interface. As far as we know, such solutions in electrohydrodynamics are established for the first time. It is worth noting that the electric field E 0 plays a key role in controlling the shapes and types of waves on the interface. [ABSTRACT FROM AUTHOR]

This study investigates the influence of fear, refuge, and migration in a predator–prey model, where the interactions between the species follow an asymmetric function response. In contrast to some other findings, we propose that prey develop an anti-predator response in response to a concentration of predators, which in turn increases the fear factor of the predators. The conditions under which all ecologically meaningful equilibrium points exist are discussed in detail. The local and global dynamics of the model are determined at all equilibrium points. The model admits several interesting results by changing the rate of fear of predators and predator aggregate sensitivity. Numerical simulations have been performed to verify our theoretical findings. We found that under certain conditions, the system appears to be losing the stability to acquire the periodic attractor when the trait-mediated direct effect of one of each (prey growth, competition, fear, and prey death). [ABSTRACT FROM AUTHOR]

The bursting with long burst duration of the pancreatic β-cells related to the diabetes is helpful to maintain the normal blood glucose concentration. Then, nonlinear dynamics underlying burst duration is an important issue, which is investigated in a theoretical model containing two slow variables (s and z) in the present paper. For the deterministic case, different shapes and sizes of the bursting trajectory show that the slow bursting is modulated by s, z, and s-nullcline in wide ranges, the medium bursting by s and z in medium ranges, and the fast bursting mainly by s in narrow ranges. Through two-parameter bifurcation analysis, the burst of the three bursting patterns terminates at saddle homoclinic orbit (SH) bifurcation curve. For the slow and medium bursting patterns, the latter part of the burst mainly runs along z-direction and closely to the saddle surface. Then, noise can induce the burst to terminate earlier than the SH via passage through the saddle surface, resulting in decreased burst duration. Compared with the drastic decrease for the medium bursting, slow bursting exhibits small reduction, since the large size induces two phases insensitive to noise. One is the latter part of the quiescent state, which runs along the s-nullcline to exhibit extra-stable dynamics, and the other is the former part of the burst, which runs far from the saddle surface. However, the fast bursting mainly runs along s-direction and far from the saddle surface exclusive the SH, then, noise can only induce small changes. Then, the different changing trends of the stochastic slow, medium, and fast bursting patterns are well explained with the different stochastic responses around different bifurcation points or critical phases. The results present dynamical mechanism for the long burst duration which is favor for the maintenance of the normal blood glucose concentration. [ABSTRACT FROM AUTHOR]

In this work, we first discuss the positive equilibrium point of the continuous predator–prey system and its stability, and we discuss the parameter conditions under which the continuous system undergoes a cusp bifurcation (Bogdanov–Takens bifurcation) of codimension two bifurcation at the positive equilibrium point. Then, we provide an insightful study of discrete predator–prey systems by the use of Euler's method, which includes square-root function responses and nonlinear prey harvesting. By synthesizing the new standard form of differential-algebraic systems, the central manifold theorem, and the bifurcation theory, we identify the specific conditions under which the system may undergo flip bifurcation and Neimark–Sacker bifurcation. In addition, codimension-two bifurcations associated with 1:2 strong resonances are analyzed by using a series of affine transformations and bifurcation theory. Through numerical simulations, we not only verify the validity and correctness of our findings, but also elucidate the frequency of trajectory bifurcations in the intervals of 2, 4, and 8 and chaotic phenomena. These findings reveal a richer and more diverse dynamic behavior of discrete differential-algebraic bioeconomic systems, which is of great theoretical and practical significance to the fields of mathematics and biology. [ABSTRACT FROM AUTHOR]

Mitigating traffic jams is a critical step for the betterment of the urban transportation system, which comprises a large number of interconnected routes to form an intricate network. To study the distinct features and complexities of vehicular flow, a network consisting of multiple-loops with a single intersection is considered a directed weighted graph. The governing equations for individual loop densities are derived using the principle of mass conservation, considering a data-driven flow-density relationship. Firstly, we examine the stability of a double-loop network and explore the traffic behavior using the macroscopic fundamental diagram (MFD) for different sets of parameters. Utilizing popular techniques of nonlinear dynamics, the existence of bistability, bifurcations, oscillations, and switching dynamics is demonstrated in the case of the triple-loop network. Further, bistability is characterized by plotting the basin of attraction diagram for the coexisting attractors. Our study reveals that an increase in the number of loop lines enriches the dynamical properties of vehicular traffic flow. It is observed that depending upon the initial density configuration, a loop network can show various phases, namely free flow, stop-and-go traffic jams, and loop congestion. Additionally, we show the presence of period-2 orbits in the case of the quadruple-loop system. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel two-delayed tri-neuron neural network (NN) with no connection between the first and third neurons. Neural networks with incomplete connections offer a range of advantages, including improved efficiency, generalisation, interpretability, and biological plausibility, making them useful in various applications across different domains. Such kinds of NNs exist in some diseases, such as epilepsy, Alzheimer's, and schizophrenia, where the neuron's connections can be broken. Our NN is defined in two different forms: one with integer-order derivatives and another with Caputo fractional derivatives. The fundamental results of existence, uniqueness, and boundedness of the solution for the proposed NN are derived. We perform the bifurcation analysis along with the stability of the initial state of the fractional-order NN, considering self-connection delay and communication delay as bifurcation parameters, respectively. The proposed NN is numerically solved by using a recently proposed L1-predictor-corrector method with its error analysis. The theoretical proofs are verified through graphical simulations. [ABSTRACT FROM AUTHOR]

In the study of continuous amensalism systems, it has been widely accepted that Michaelis–Menten type harvesting has a significant impact on the survival and extinction of species. However, scholars have not yet studied discrete amenslism models that include Michaelis–Menten type harvesting. To characterize such dynamics, a discrete amensalism system with Michaelis–Menten type harvesting for the second species is investigated. Firstly, we study the existence and stability of all possible equilibrium points. Under different parameters, there are two stable equilibria, which means that the model is not always globally stable. Then, the conditions of various types of bifurcations likely: pitchfork bifurcations, transcritical bifurcations, fold bifurcations, and flip bifurcations have been established. In addition, a global dynamics analysis of the model is also conducted. Finally, the significance of Michaelis–Menten type harvesting in species relationships is shown by numerical simulations. Although proper harvesting reduces the density of the second species, it favors the stable coexistence of both species and excessive harvesting leads directly to the extinction of the second species. Therefore, the results of this paper can provide a reference for research on how to maximize harvesting without destroying the ecological balance of the species. [ABSTRACT FROM AUTHOR]

A paradoxical nonlinear phenomenon called post-inhibitory facilitation (PIF) has been observed in the superior olive neuron for precise sound localization, which means that an inhibitory synaptic current appearing earlier than an excitatory one does not suppress but facilitates a spike for a short interval between the two currents. Although the PIF is reproduced for type III excitability/non-bifurcation and mediated by a fast low-threshold potassium current (IKLT), contradictorily, explained with a negative threshold related to type II excitability/Hopf bifurcation, even if in the absence of the IKLT. In the present paper, explanations to the seemingly contradictory nonlinear and ionic current mechanisms for the PIF are presented in a modified model containing the IKLT. Firstly, the modified model exhibits Hopf bifurcation/type II for weak or zero IKLT, in addition to non-bifurcation/type III for strong IKLT which resembles the original models. Secondly, the PIF can be evoked for types III and II with a positive threshold, which presents novel conditions for the PIF. Thirdly, with the excitatory current considered, some traditional positive thresholds become novel negative thresholds, which presents successful explanations to the novel PIF modulated by the IKLT and the inhibitory and excitatory synapses. The novel PIF appears for a strong and relatively slow inhibitory synaptic current which can induce membrane potential reduced to run across the negative threshold, while not for weak or fast inhibitory current or not for novel positive thresholds related to fast excitatory synapses. Finally, the PIF with short time interval appears for type III with fast dynamics, which is mainly mediated by the fast IKLT, resembling the experiment. The PIF with wide interval appears for type II with slow dynamics, which is mediated by the weak IKLT and/or the slow leak current (IL), presenting a novel current to mediate the PIF. The bifurcation/excitability, novel threshold surface, IKLT and IL, and inhibitory and excitatory synapses present a comprehensive viewpoint on the PIF and the potential modulations to obtain the PIF with short interval for the precise sound localization. [ABSTRACT FROM AUTHOR]

This paper addresses the challenging issues of transmission quality degradation and difficulty in obtaining dynamic response characteristics caused by the nonlinear behavior of non-circular planetary gear systems (NPG). A dynamic model for NPG was developed, encompassing axial elastic displacement, backlash, tooth surface friction, time-varying meshing stiffness, and viscoelastic damping. Fourier fitting matrices for time-varying mesh stiffness and polynomial models for dynamic backlash in non-circular gears were acquired to enhance model precision. Various analysis techniques including phase trajectory diagrams, bifurcation diagrams, time history diagrams, Poincaré mapping diagrams, and phase amplitude frequency characteristic curves were used to evaluate the nonlinear behavior of NPGs. Research results indicate that increasing the damping ratio benefits frequency response bandwidth, reduces phase lag, and improves system stability. The friction coefficient on the surface of non-circular gears also plays a role in ensuring the stability and phase consistency of NGP, although excessive coefficients can induce chaos. The output solar gear is more sensitive to internal excitation, with higher internal excitation leading to stronger system chaos. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the dynamics of a class of discrete predator–prey model with alternative prey. We prove the boundedness of the solution, the existence and local/global stability of equilibrium points of the model, and verify the existence of flip bifurcation and Neimark-Sacker bifurcation. In addition, we use the maximum Lyapunov exponent and isoperimetric diagrams to verify the existence of periodic structures namely Arnold tongue and the shrimp-shaped structures in bi-parameter spaces of a class of predator–prey model. [ABSTRACT FROM AUTHOR]

Analyzing the nonlinear characteristics of dual-rotor systems under thermo-mechanical (TM) coupling situations is critical, as operational conditions should be accurately determined, to avoid potential thermally-induced failures. This paper proposes the coupled TM model of a dual-rotor system, which considers multiple nonlinearities and heat generation of four bearings that couple the mechanical and thermal fields. Heat dissipation controlled by lubricant flow rates is introduced into the model to simulate different TM coupling degrees. Nonlinear phenomena and stability evolution are analyzed by the modified incremental harmonic balance method (IHB) at primary resonance regions. An increase in TM coupling degrees can lead to more bifurcation points, resonance regions with lower frequencies, larger vibration responses, and unstable regions. It can also transform resonance hysteresis phenomena into more complex nonlinear phenomena and some saddle-node bifurcation points into Neimark–Sacker bifurcation points. The reason for these transformations is that the effective radial clearance (RC) of bearings changes with rotation speed and thermal expansion. Temperature nonlinearities are induced by the radial bearing loads and the lubricant viscosity, which are investigated by various generalized nonlinear thermal forces. These findings can help further understand nonlinear coupled TM problems of complex dual-rotor systems. [ABSTRACT FROM AUTHOR]

Rumor propagation in social networks disrupts people's lives, thus affecting the stability and development of society. To explore the rumor propagation mechanism and control its spread, a novel IRLTS (Ignorant–Rumor-Spreader–Lurker–Truth-Spreader–Stifler) rumor propagation model is proposed, which considers the influence of lurking psychology and the truth of rumors. First, the basic reproduction number and the equilibria of the proposed model are computed. Second, the stability of the equilibria is demonstrated, and the trans-critical bifurcation at the equilibria is analyzed. Finally, we corroborate the theoretical results and the influence of key parameters through numerical simulations, perform sensitivity analysis of the basic reproduction number, and evaluate the proposed model through comparative experiments. Furthermore, the proposed model is applied to an actual rumor dataset to verify its validity. We employ the least squares method to estimate the proposed model's parameters, which are subsequently utilized to forecast rumor propagation trends. The R-squared value for the proposed model on the actual dataset is 0.9567. The outcomes indicate the model is valid and capable of predicting rumor spreading trends, thereby providing theoretical support for formulating strategies to control rumor propagation. [ABSTRACT FROM AUTHOR]

We studied the nonlinear dynamics of a shunted inductive Josephson junction coupled to a diode and a negative conductance. Taking into account the non-harmonicity of the junction, based on Kirchhoff's laws, we have developed the mathematical model which governs the dynamics of the circuit. The fixed points of the system are determined, and their stabilities are analyzed using the Routh–Hurwitz criterion. The bifurcation and transition to chaos of the model are studied using the the fourth-order Runge–Kutta method; the system displays a rich dynamics. The range of values of each parameter leading to periodic and chaotic electrical oscillations is obtained through the analysis of the effect of these parameters on each type of dynamics. Finally, the implementation by microcontroller is carried out in order to experimentally verify the different dynamics obtained numerically. [ABSTRACT FROM AUTHOR]

This study on Lossy Nonlinear Electrical Transmission Line Models (LNETLM) highlights several novel contributions: (1) Introducing the modified G ′ G 2 -expansion method applied to LNETLM with a beta derivative, providing precise soliton solutions previously undocumented in the field; (2) Through extensive computer simulations, uncovering diverse wave phenomena such as bright, solitary, and parabolic solitons, alongside oscillatory singular waves, advancing the characterization of wave dynamics within LNETLM; (3) Contrasting conformable, M-truncated derivatives with the beta derivative, revealing the unique advantages of the beta derivative approach in modeling electrical transmission line systems; (4) Transforming the LNETLM equation into a Hamiltonian system, analyzing phase portraits, Chaos, and bifurcation phenomena, enhancing understanding of system dynamics and stability; (5) Expanding the knowledge frontier in lossy electrical transmission line models, with implications for theoretical understanding and practical applications in signal transmission and communication systems. In conclusion, this research underscores the potential of pulse-like solitons for enhancing data transmission rates in telecommunication systems. The insights gained pave the way for advancements in telecommunication technology, promising improved efficiency and performance. [ABSTRACT FROM AUTHOR]

The classical prey-predator model assumes that prey species has no life history. But many species whose individuals have a life history with two classes, namely immature and mature. Since, immature prey can be easily captured by the predators because of their short life experiences and less activity, while predators make some extra effort to catch mature prey. So, in this paper, a mathematical model is proposed to study the complex behaviour of a delayed prey-predator system with stage in prey population. We have included a maturation delay which is the time required for immature prey to join mature class and a cooperative hunting delay which is the time taken by predator to cooperate and attack on prey. Stability analysis has been addressed with different pairs of delays. Hopf bifurcation analysis with its directions is also performed. Global stability of predator free equilibrium point has been examined analytically and shown graphically. Both maturity and cooperative hunting delay significantly influence the system dynamics and produce multi-times stability switches. The presence of cooperative hunting delay of predators reduces the maturation time of prey due to which prey becomes mature very fast. Increase in cooperative hunting rate of predators suppress mature prey populations. Numerical simulations have been performed in various ways to support our theoretical findings. [ABSTRACT FROM AUTHOR]

The enduring stability exhibited by solitons is strikingly demonstrated as a soliton pulse traverses an ideal lossless optical fibre, thereby highlighting a compelling attribute for their integration into optical communication systems. In this study, we employ the improved Bernoulli sub-equation function method to systematically derive stable and functionally robust soliton solutions for the Riemann wave equation. The stability of the soliton solutions is demonstrated through their composition involving hyperbolic and exponential functions, among others. The physical significance of these solutions is meticulously analyzed by presenting 2D and 3D graphs that illustrate the behaviour of the solutions for specific parameter values. Additionally, a comprehensive investigation into the influence of the nonlinear parameter on the wave velocity and solution curve is conducted. The study further explores local stability through bifurcation and phase plane analysis. Our findings affirm the reliability of the improved Bernoulli sub-equation function method and suggest its potential application in future endeavours to uncover diverse and novel soliton solutions for other nonlinear evolution equations encountered in the realms of mathematical physics and engineering. [ABSTRACT FROM AUTHOR]

One-dimensional discrete-time population models, such as those that involve Logistic or Ricker growth, can exhibit periodic and chaotic dynamics. Expanding the system by one dimension to incorporate epidemiological interactions causes an interesting complexity of new behaviors. Here, we examine a discrete-time two-dimensional susceptible-infectious (SI) model with Ricker growth and show that the introduction of infection can not only produce a distinctly different bifurcation structure than that of the underlying disease-free system but also lead to counter-intuitive increases in population size. We use numerical bifurcation analysis to determine the influence of infection on the location and types of bifurcations. In addition, we examine the appearance and extent of a phenomenon known as the 'hydra effect,' i.e., increases in total population size when factors, such as mortality, that act negatively on a population, are increased. Previous work, primarily focused on dynamics at fixed points, showed that the introduction of infection that reduces fecundity to the SI model can lead to a so-called 'infection-induced hydra effect.' Our work shows that even in such a simple two-dimensional SI model, the introduction of infection that alters fecundity or mortality can produce dynamics can lead to the appearance of a hydra effect, particularly when the disease-free population is at a cycle. [ABSTRACT FROM AUTHOR]

This paper explores the nonlinear dynamic responses and bifurcations of the truncated sandwich simply supported porous conical shell with varying thickness under 1:1 internal resonance. Two skins with carbon fiber and a core with porous aluminum foam, which has an exponentially variable thickness along the generator and various porosity distribution types along the core thickness, make up the sandwich shell structure with varying stiffness. The porous shell structure is affected by a combination of the in-plane load, transverse excitation, thermal stress and aerodynamic force, which is formulated by employing first-order piston theory with a modified term for curvature. By way of FSDT, von-Karman geometrical formulations, Hamilton's principle and Galerkin procedure, the nonlinear dynamic formulations in ordinary differential form for the variable stiffness porous sandwich shell structure are identified. The averaged equations in polar and Cartesian coordinate forms for the sandwich structure under the combined circumstance of 1:1 internal resonance, first-order main resonance and 1/2 subharmonic resonance are determined by multiple-scale technique. The frequency-amplitude and force–amplitude characteristic curves, phase portraits, time history and bifurcation diagrams are exhibited by numerical simulation. The impacts of the damping coefficient, detuning parameters, temperature increment, transverse and in-plane excitations on the nonlinear dynamics and bifurcation behaviors of variable thickness sandwich porous conical shell are demonstrated. [ABSTRACT FROM AUTHOR]

The primary parametric resonance of a ferromagnetic rectangular thin plate with axial time-varying velocity in the air-gap field is researched. Through building the analytical model of air-gap field between the elastic plate and armature, the dynamic changes of air-gap field during resonance are determined. On account of electromagnetic boundary conditions, intraplate magnetic field distribution under the magnetization effect is obtained. Within the framework of magneto-electro-elastic theory and Hamilton principle, the motion governing equation of the axially moving ferromagnetic plate subjected to air-gap magnetizing force is finally deduced. For the simply supported constraint, applying the Galerkin method, the ordinary differential vibration equation of plate under parametric excitations is obtained by separating time–space variable. The multiscale method is applied to investigate the parametric vibration behavior of plate. Based on Lyapunov stability theory, the stability criterion of steady-state amplitude solutions is acquired. Through numerical methods, the correctness of analytical results is verified. The effects of armature and time-varying parameters on the static deflection, steady-state response amplitude, and the regional distribution of stable solutions are studied. The dynamic stability and bifurcation characteristics of the system are explored. Eventually, the results reveal that the static deflection caused by the air-gap magnetizing force makes the thin plate more rigid. The increase of armature and time-varying parameters causes the stable solutions to reduce and then grow by affecting the stiffness and excitation. At high magnetic potential amplitude, high velocity, and small tension, the system motion exhibits prominent chaotic characteristics. [ABSTRACT FROM AUTHOR]

In this study, we consider analytical and numerical exploration of the dynamics of a weakly nonlinear piecewise linear (PWL) Mathieu equation with a time delay. A study of such dynamical systems requires finding the time instants of crossing between the two linear states. Moreover, the time delay further complicates the system dynamics by making it infinite-dimensional. In this study, we employ the method of averaging, incorporating non-analytic PWL basis functions along with corresponding algebraic techniques. This approach enables the application of the method of averaging to the resonantly forced, essentially nonlinear PWL Mathieu equation. We herein show that the amplitude evolution and the bifurcation exhibited by the periodic solutions are very well captured by the method of averaging and is a potent tool in studying this class of dynamical systems. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the influence of the nonlocal intraspecific competition by the prey in a general predator–prey system on the stability and spatiotemporal dynamics, where the nonlocal kernel function is characterized by the top-hat function. It has been shown that when the nonlocal competition radius is sufficiently small, the nonlocal item has no impact on the stability of the spatially homogeneous steady state, but when the nonlocal competition radius is larger than some critical value, various types of spatiotemporal patterns occur via the bifurcation. The analytical conditions for the occurrence of Turing bifurcation, Hopf bifurcation and Turing–Hopf bifurcation are clearly determined. The spatially inhomogeneous steady states and inhomogeneous periodic patterns are found for the nonlocal Rosenzweig–MacArthur and Lotka–Volterra models with the top-hat kernel function. [ABSTRACT FROM AUTHOR]