Search

The objective of this work is to investigate the complex dynamics of a discrete predator–prey system using the method of piecewise constant argument for discretization. An analysis is conducted to examine the presence and stability of fixed points. Furthermore, the system is shown to undergo period-doubling (PD) and Neimark–Sacker (NS) bifurcations by the use of center manifold and bifurcation theories. The feedback and hybrid control strategies are used to regulate the system's bifurcating and chaotic behaviors. Both strategies seem to be effective in managing bifurcation and chaos inside the system. Finally, the main results are validated by numerical evidence. Parameters of the system are varied to produce time graphs, phase portraits, bifurcation diagrams, and maximum Lyapunov exponent (MLE) graphs. The discrete model displays rich dynamics, as seen in the numerical simulations and graphs, indicating a complex and chaotic system. [ABSTRACT FROM AUTHOR]

This paper is dedicated to exterminate the ( 2 + 1 )-dimensional integro-differential Jaulent–Miodek equation, a prominent model linked to energy-dependent Schrödinger potential. This equation is employed in a wide array of disciplines, including fluid dynamics, condensed matter physics, optics, and various engineering systems. First, we are given to derive exact wave solutions for the ( 2 + 1 )-dimensional integro-differential Jaulent–Miodek equation using an innovative approach known as the new modified unified auxiliary equation method. We offer a comprehensive visual representation and some exact solutions propagate of these solutions in 2D and 3D plots, using various parametric values for a comprehensive analysis. In addition, we employed the planar dynamical system method to study phase portraits and chaotic behavior of the governing equation. Through the analysis of phase portraits, the sensitivity of dynamic system is examined. The chaotic behavior of dynamic system is examined by time series, Poincaré section, and 2D, 3D phase portraits. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a discrete-time prey-predator model. The model is formulated by using the piecewise constant argument method for differential equations and taking into account Holling type III. The existence and local behavior of equilibria are studied. We established that the system experienced both Neimark-Sacker and perioddoubling bifurcations analytically by using bifurcation theory and the center manifold theorem. In order to control chaos and bifurcations, the state feedback method is implemented. Numerical simulations are also provided for the theoretical discussion. [ABSTRACT FROM AUTHOR]

In this paper, the Caputo fractional derivative is assumed to be the prey–predator model. In order to create Caputo fractional differential equations for the prey–predator model, a discretization process is first used. The fixed points of the model are categorized topologically. We identify requirements for the fixed points of the suggested prey–predator model's local asymptotic stability. We demonstrate analytically that, under specific parametric conditions, a fractional order prey–predator model supports both a Neimark–Sacker (NS) bifurcation and a Flip bifurcation. We present evidence for NS and Flip bifurcations using central manifold and bifurcation theory. The parameter values and the initial conditions have been found to have a profound impact on the dynamical behavior of the fractional order prey–predator model. As the bifurcation parameter is increased, the system displays chaotic behavior. Numerical simulations are shown to demonstrate chaotic behaviors like bifurcations, phase portraits, invariant closed cycles, and attractive chaotic sets in addition to validating analytical conclusions. The suggested prey–predator dynamical system's chaotic behavior will be controlled by the OGY and hybrid control methodology, which will also visualize the chaotic state for various biological parameters. [ABSTRACT FROM AUTHOR]

Qualitative analysis in mathematical modeling has become an important research area within the broad domain of nonlinear sciences. In the realm of qualitative analysis, the bifurcation method is one of the significant approaches for studying the structure of orbits in nonlinear dynamical systems. To apply the bifurcation method to the (2 + 1)-dimensional double-chain Deoxyribonucleic Acid system with beta derivative, the bifurcations of phase portraits and chaotic behaviors, combined with sensitivity and multi-stability analysis of this system, are examined. Initially, the bifurcations of phase portraits are visually identified at the obtained equilibrium points of a planar dynamical system via both Hamiltonian and Jacobian algorithms. The obtained results indicate Jacobian algorithm is more efficient in identifying the stability of bifurcations than the Hamiltonian algorithm for this system. Subsequently, by introducing an external perturbation term into the planar dynamical system, the chaotic behavior is effectively identified by using a variety of tools, such as two- and three-dimensional phase portraits, time series, Lyapunov exponents, and Poincaré maps. The findings suggest that the perturbed dynamical system deviates from regular patterns and exhibits behavior ranging from periodic to quasi-periodic and from quasi-periodic to chaotic. Finally, the sensitivity and multi-stability of the system are examined using the Runge-Kutta method to assess the model's response to minor variations in initial conditions through numerical solutions, revealing that the model is sensitive and multi-stable. The outcomes of this study will enhance a relationship between applied mathematicians and experimental biologists, helping to explore hidden features of Deoxyribonucleic Acid through the studied model.

The objective of this study was to analyze the complex dynamics of a discrete-time predator-prey system by using the piecewise constant argument technique. The existence and stability of fixed points were examined. It was shown that the system experienced period-doubling (PD) and Neimark-Sacker (NS) bifurcations at the positive fixed point by using the center manifold and bifurcation theory. The management of the system's bifurcating and fluctuating behavior may be controlled via the use of feedback and hybrid control approaches. Both methods were effective in controlling bifurcation and chaos. Furthermore, we used numerical simulations to empirically validate our theoretical findings. The chaotic behaviors of the system were recognized through bifurcation diagrams and maximum Lyapunov exponent graphs. The stability of the positive fixed point within the optimal prey growth rate range A1 < a < A2 was highlighted by our observations. When the value of a falls below a certain threshold A1, it becomes challenging to effectively sustain prey populations in the face of predation, thereby affecting the survival of predators. When the growth rate surpasses a specific threshold denoted as A2, it initiates a phase of rapid expansion. Predators initially benefit from this phase because it supplies them with sufficient food. Subsequently, resource depletion could occur, potentially resulting in long-term consequences for populations of both the predator and prey. Therefore, a moderate amount of prey's growth rate was beneficial for both predator and prey populations. [ABSTRACT FROM AUTHOR]

This paper presents a study of a discrete prey–predator model with additive Allee effect. The model is discretized using the forward Euler method, and the system is analyzed using bifurcation theory and chaos control. The equilibrium point of the discrete system is obtained through equilibrium analysis, and the stability of the equilibrium point is determined by analyzing the parameter conditions. The study also establishes the existence and direction of Neimark–Sacker bifurcation at the positive equilibrium point. The paper proposes two control strategies to manage chaotic behavior and Neimark–Sacker bifurcation: exponential control and hybrid feedback control. These control methods are demonstrated to be effective in controlling the chaotic behavior and bifurcation of the system through numerical simulation. Overall, the results of the study provide important insights into the dynamics of the discrete prey–predator model with additive Allee effect, as well as effective methods for controlling chaos and bifurcation in the system. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of process faults in the Lorenz system that can affect any of the system parameters and cause the system to exhibit various behaviors. In this paper, the homoclinic orbits in the Lorenz system are described and then the occurrence of process faults in the system is investigated that can cause a homoclinic explosion, bifurcation, change of fixed point, or even instability in the system. In such systems, where a small change in one of the parameters causes large changes in the behavior of the system, to prevent disaster in industrial systems and also to stop the propagation of faults in the system, the faults must be identified as soon as possible. In this paper, the states in the system are estimated by using a reduced-order observer, and the faults are detected. The purpose of this article is to recognize the change in behavior of this system in the face of this type of fault and to express the importance of timely detection and identification of faults in the system so as not to lead to failure and disaster in industrial systems. Finally, the effect of process fault, disturbance, and sensor fault are investigated simultaneously and the states and faults in the system are estimated. [ABSTRACT FROM AUTHOR]

This study explores the application of random matrices to track chaotic dynamics within the Chirikov standard map. Our findings highlight the potential of matrices exhibiting Wishart-like characteristics, combined with statistical insights from their eigenvalue density, as a promising avenue for chaos monitoring. Inspired by a technique originally designed for detecting phase transitions in spin systems, we successfully adapted and applied it to identify analogous transformative patterns in the context of the Chirikov standard map. Leveraging the precision previously demonstrated in localizing critical points within magnetic systems in our prior research, our method accurately pinpoints the Chirikov resonance overlap criterion for the chaos boundary at K ≈ 2.43 , reinforcing its effectiveness. Additionally, we verified our findings by employing a combined approach that incorporates Lyapunov exponents and bifurcation diagrams. Lastly, we demonstrate the adaptability of our technique to other maps, establishing its capability to capture the transition to chaos, as evidenced in the logistic map. [ABSTRACT FROM AUTHOR]

In this paper, a fractional density-dependent prey-predator model has been considered. Certain reading of local and global stabilities of an equilibrium point of a system was extracted and conducted by applying fractional systems' stability theorems along with Lyapunov functions. Meanwhile, the persistence of the aforementioned system has been discussed and claimed to imply a local asymptotic stability for the given positive equilibrium point. Moreover, the presented model was extended to a periodic impulsive model for the prey population. Such an expansion was implemented through the periodic catching of the prey species and the periodic releasing of the predator population. By studying the effect of changing some of the system's parameters and drawing their bifurcation diagram, it was observed that different periodic solutions appear in the system. However, the effect of an impulse on the system subjects the system to various dynamic changes and makes it experience behaviors including cycles, period-doubling bifurcation, chaos and coexistence as well. Finally, by comparing the fractional system with the classic one, it has been concluded that the fractional system is more stable than its classical one. [ABSTRACT FROM AUTHOR]

The dynamics of a discrete Holling–Tanner model with Beddington–DeAngelis functional response is studied. The permanence and local stability of fixed points for the model are derived. The center manifold theorem and bifurcation theory are used to show that the model can undergo flip and Hopf bifurcations. Codimension-two bifurcation associated with 1:2 resonance is analyzed by applying the bifurcation theory. Numerical simulations are performed not only to verify the correctness of theoretical analysis but to explore complex dynamical behaviors such as period-6, 7, 10, 12 orbits, a cascade of period-doubling, quasi-periodic orbits, and the chaotic sets. The maximum Lyapunov exponents validate the chaotic dynamical behaviors of the system. The feedback control method is considered to stabilize the chaotic orbits. These complex dynamical behaviors imply that the coexistence of predator and prey may produce very complex patterns. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a nonlinear discrete prey-predator system with fear effects. The existence, local stability and boundedness of positive equilibrium point are discussed. Using the center manifold theorem and bifurcation theory, the conditions for the existence of flip bifurcation and Neimark-Sacker bifurcation in the interior of R²+ are established. Furthermore, the numerical simulations not only show complex dynamical behaviors, but also verify our analysis results. A feedback control strategy is employed to control bifurcation and chaos in the system. [ABSTRACT FROM AUTHOR]

This paper analyses a discrete-time Michaelis-Menten type harvested fishery model in the presence of toxicity. Boundary and interior (positive) fixed points are examined. Using an iteration scheme and the comparison principle of difference equations, we determined the sufficient condition for global stability of the interior fixed point. It is shown that the sufficient criterion for Neimark-Sacker bifurcation and flip bifurcation can be established. It is observed that the system behaves in a chaotic manner when a specific set of system parameters is selected, which are controlled by a hybrid control method. Examples are cited to illustrate our conclusions. [ABSTRACT FROM AUTHOR]

In this work, an analytical and numerical analysis of the transition to chaos in five nonlinear systems of ordinary and partial differential equations, which are models of autocatalytic chemical processes and interacting populations, is carried out. It is shown analytically and numerically that in all considered systems of equations, further complication of the dynamics of solutions and the transition to chemical and biological turbulence is carried out in full accordance with the universal Feigenbaum-Sharkovsky-Magnitskii bifurcation theory through subharmonic and homoclinic cascades of bifurcations of stable limit cycles. In this case, irregular (chaotic) attractors in all cases are exclusively singular attractors in the sense of the FShM theory. The obtained results once again indicate the wide applicability of the universal bifurcation FShM theory for describing laminar–turbulent transitions to chaotic dynamics in complex nonlinear systems of differential equations and that chaos in the system can be confirmed only by detection of some main cycles or tori in accordance with the universal bifurcation diagram presented in the article. [ABSTRACT FROM AUTHOR]

In this paper, we explore local dynamic characteristics, bifurcations and control in the discrete activator-inhibitor system. More specifically, it is proved that discrete-time activator-inhibitor system has an interior equilibrium solution. Then, by using linear stability theory, local dynamics with different topological classifications for the interior equilibrium solution are investigated. It is investigated that for the interior equilibrium solution, discrete activator-inhibitor system undergoes Neimark-Sacker and flip bifurcations. Further chaos control is studied by the feedback control method. Finally, numerical simulations are presented to validate the obtained theoretical results. [ABSTRACT FROM AUTHOR]

The Schnakenberg model is thought to be the Caputo fractional derivative. A discretization process is first used to create caputo fractional differential equations for the Schnakenberg model. The fixed points in the model are categorized topologically. Then, we show analytically that a fractional order Schnakenberg model supports a Neimark-Sacker (NS) bifurcation and a Flip-bifurcation under certain parametric conditions. Using central manifold and bifurcation theory, we demonstrate the presence and direction of NS and Flip bifurcations. The parameter values and the initial conditions have been found to profoundly impact the dynamical behavior of the fractional order Schnakenberg model. Numerical simulations demonstrate chaotic behaviors like bifurcations, phase portraits, period 2; 4; 7; 8; 10; 16; 20 and 40 orbits, invariant closed cycles, and attractive chaotic sets in addition to validating analytical conclusions. To support the system's chaotic characteristics, we also quantitatively compute the maximal Lyapunov exponents and fractal dimensions. Finally, the chaotic trajectory of the system is stopped using the OGY approach, hybrid control method, and state feedback method. [ABSTRACT FROM AUTHOR]

Numerous field data and experiments on the perching birds or songbirds show that the fear of predators can cause significant changes in the prey population. Fear of predatory populations increases the chances of survival of the prey population, and this can greatly reduce the reproduction of the prey population. The influence of fear has contributed a leading role in both the environmental biology and theoretical ecology. Taking into account the interaction of predator–prey with non-overlapping generations, a discrete-time model is proposed and studied. Keeping in mind the biological feasibility of species, the existence of fixed points is studied along with the local asymptotic behavior of the proposed model around these fixed points. Furthermore, taking into account the oscillatory behavior of the model, various types of bifurcations are analyzed about biologically feasible fixed points with an application of center manifold theory and bifurcation theory of normal forms. Existence of chaos is discussed, and fluctuating and chaotic behavior of the system is controlled through implementation of different chaos control procedures. The illustration of theoretical discussion is carried out via validation of observed experimental field data and appropriate numerical simulation. [ABSTRACT FROM AUTHOR]

The purpose of this study is to describe a methodology for assessing the geotechnical stability of agricultural facilities, enabling prediction of the state of the geotechnical system, taking into account the influence of external factors and combinations of reactions of the geotechnical system under study. According to the methodology, the heterogeneous geotechnical monitoring data obtained are used in an adjusted geotechnical system model, allowing a bifurcation analysis to be carried out. The bifurcation analysis determines critical values of influencing factors, and the limits of stability of the geotechnical system studied parameters are adjusted. The developed methodology was used to assess and predict the geotechnical stability of agricultural facilities during the processing of geoelectric, resistive acoustic, accelerometric and strain-gauge control data obtained in the period from 2016 to 2021. A feature of the geotechnical system under study is the periodic flooding of the building basement caused by the processes of reclamation and irrigation, leading to changes in the groundwater level. The results show that the permissible calculated elastic limit of the foundation elements (32.2–35.1 MPa) before the loss of stability should be significantly reduced with a change in the water content coefficient (W) of the soil base: at W = 0.15 Eb = 30.7–32.0 MPa; at W = 0.35 Eb = 26.8–28.2 MPa; at W = 0.55 Eb = 24.9–25.3 MPa. [ABSTRACT FROM AUTHOR]

We disclose a new class of patterns, called patched patterns, in arrays of non-locally coupled excitable units with attractive and repulsive interactions. The self-organization process involves the formation of two types of patches, majority and minority ones, characterized by uniform average spiking frequencies. Patched patterns may be temporally periodic, quasiperiodic, or chaotic, whereby chaotic patterns may further develop interfaces comprised of units with average frequencies in between those of majority and minority patches. Using chaos and bifurcation theory, we demonstrate that chaos typically emerges via a torus breakup and identify the secondary bifurcation that gives rise to chaotic interfaces. It is shown that the maximal Lyapunov exponent of chaotic patched patterns does not decay, but rather converges to a finite value with system size. Patched patterns with a smaller wavenumber may exhibit diffusive motion of chaotic interfaces, similar to that of the incoherent part of chimeras. [ABSTRACT FROM AUTHOR]

Copyright of Erzincan University Journal of Science & Technology is the property of Erzincan Binali Yildirim Universitesi and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper concerned with a diffusive predator-prey model with fear effect. First, some basic dynamics of system is analyzed. Then based on stability analysis, we derive some conditions for stability and bifurcation of constant steady state. Furthermore, we derive some results on the existence and nonexistence of nonconstant steady states of this model by considering the effect of diffusion. Finally, we present some numerical simulations to verify our theoretical results. By mathematical and numerical analyses, we find that the fear can prevent the occurrence of limit cycle oscillation and increase the stability of the system, and the diffusion can also induce the chaos in the system. [ABSTRACT FROM AUTHOR]

We have applied the Melnikov criterion to examine a homoclinic bifurcation and transition to chaos in the Duffing oscillator driven by different forms of periodic piecewise linear forces. The periodic piecewise linear forces considered are triangular, hat, trapezium, quadratic and rectangular types of forces. For all the forces, an analytical threshold condition for the homoclinic transition to chaos is derived using Melnikov method and Melnikov threshold curves are drawn in a parameter space. Using the Melnikov threshold curves, we have found a critical forcing amplitude fc above which the system may behave chaotically. We have analyzed both analytically and numerically the homoclinic transition to chaos in the Duffing system with ε-parametric force also. The predictions from Melnikov method have been further verified numerically by integrating the governing equation and finding areas of chaotic behaviour. [ABSTRACT FROM AUTHOR]

Purpose: The coupling system of brake disc and brake sub-system responds in a variety of nonlinear dynamics manner under low-speed braking condition. In this article we aim to obtain the bifurcation and chaotic behavior of vehicle brake system under this condition. Methods: We established a pure brake condition 4-DOF differential equations of torsional vibration in this paper based on Crowther's model, which predicts the existence of chaotic stick-slip vibration. Based on this model, by means of numerical methods, we have calculated firstly the low-speed bifurcation characteristics of the brake disc and brake sub-system angular velocity difference relative to vehicle speed, and secondly the effects of system parameters on the bifurcation. Material: Metal type, semi-metallic type, non-metallic type friction material. Results: The results showed that: brake disc and brake sub-system angular velocity difference exhibits chaotic vibration in the low-speed zone. With the increase of inertia ratio of brake sub-system and brake disc, system vibrations changed from periodic doubling bifurcation to chaos, then inversed back to doubling period and single period stick-slip motions. With the increase of ratio of the kinetic friction coefficient and the static friction coefficient, system vibrations changed from chaotic stick-slip motions to single period stick-slip motions. With the increase of brake pressure, the system stick-slip vibrations changed from doubling bifurcation to chaos, which worsened the vehicle chatter. Conclusions: The results can provide theoretical guidance for parameter design, which can optimize the chaos interval, but we need further experiments to explore and study. [ABSTRACT FROM AUTHOR]

This article investigates a prey–predator model incorporating a novel refuge proportional to prey and inverse proportion to the predator. We find conditions for the local asymptotic stability of fixed points of the proposed prey–predator model. This article presents Neimark–Sacker bifurcation (NSB) and period‐doubling bifurcation (PDB) at particular parameter values for positive equilibrium points of the proposed refuge‐based prey–predator system. The system exhibits the chaotic dynamics at increasing values of the bifurcation parameter. The hybrid control methodology will control the chaos of the proposed prey–predator dynamical system and discuss the chaotic situation for different biological parameters through graphical analysis. Numerical simulations support the theoretical outcome and long‐term chaotic behavior over a broad range of parameters. [ABSTRACT FROM AUTHOR]

This paper is devoted to study dynamical behaviours of the fractional-order BazykinBerezovskaya model and its discretization. The fractional derivative has been described in the Caputo sense. We show that the discretized system, exhibits more complicated dynamical behaviours than its corresponding fractional-order model. Specially, in the discretized model Neimark-Sacker and flip bifurcations and also chaos phenomena will happen. In the final part, some numerical simulations verify the analytical results. [ABSTRACT FROM AUTHOR]

This paper deals with the dynamic behavior of a prey predator model obtained by the forward Euler method. We investigate the complex dynamics of discrete-time prey-predator system related to predator population which is subject to the effects of harvesting. The stability of equilibrium point of the model and also the existence and the direction of Neimark-Sacker bifurcation are analyzed. We show that the system undergoes Neimark-Sacker bifurcations by using center manifold theorem and bifurcation theory. A state feedback method is applied in order to control the Neimark-Sacker bifurcation. Moreover, numerical simulations are carried out to demonstrate the theoretical results obtained for stability, bifurcation and chaos control strategy. [ABSTRACT FROM AUTHOR]

We investigate the dynamics of two‐dimensional discrete‐time model of leaf quality and larch budmoth interaction with Ricker equation. More precisely, the qualitative behavior of larch budmoth model is discussed in which the effect of food source upon the moth population is through intrinsic growth rate. We find the parametric conditions for local asymptotic stability of the unique positive fixed point. It is also proved that under certain parametric conditions, the system undergoes period‐doubling bifurcation with the help of center manifold theory. The parametric conditions for existence and direction of Neimark‐Sacker bifurcation at positive fixed point is investigated with the help of standard mathematical techniques of bifurcation theory. The chaos control in the system is discussed through implementation of hybrid control methodology. Finally, numerical simulations are provided to illustrate theoretical results. These results of numerical simulations demonstrate chaotic long‐term behavior over a broad range of parameters. The computation of the maximum Lyapunov exponents confirms the presence of chaotic behavior in the system. [ABSTRACT FROM AUTHOR]

Nowadays, the research is being devoted to the development of rapid and precise maximum power point tracking (MPPT) for various photovoltaic (PV) applications. However, the constraints imposed by size, cost, efficiency, and tracking performances essentially limit the application of conventional MPPT techniques and their analysis methodologies. This study recommends a fast and robust analogue PV MPPT for the battery charging system using dc-dc boost converter. The fast dynamic performances with absolute robustness are ensured here by fast-scale stability analysis of actually switched boost converter using the concepts based on non-linear dynamics and bifurcation theory. Such concepts not only provide the information to design an efficient MPPT system under rapidly changing environmental conditions but also guarantee the system to operate either in period-1 or chaotic mode. The theoretical and mathematical analyses are experimentally verified using a prototype PV battery charging system utilising dc-dc boost converter. It is presented that operating the MPPT system in chaos not only yields the broader power spectrum with reduced spectral peaks at the multiples of converter's switching frequency but also exhibits high overall conversion efficiency. [ABSTRACT FROM AUTHOR]

In this article, the dynamic characteristic of linkage bobbing machine with balanced double-mass bearing periodic excitation and damping is studied. Subharmonic Melnikov function of the oscillating periodic orbits is computed through Melnikov method. And, the relationship of parameters is given when the subharmonic bifurcation occurs. The periodic motion is simulated. Through analysis, as the excitation frequency varies, the periodic motion undergoes flip bifurcations and subharmonic bifurcation occurs, which finally leads to chaos. In addition, the ultra-subharmonic solution of the system is given. [ABSTRACT FROM AUTHOR]

Abstract Epilepsy is a prevalent neurological disorder with symptoms characterized by abnormal discharge in the brain. According to the classification of the International League Against Epilepsy (ILAE) Commission, temporal lobe epilepsy is the most common type of epilepsy accounting for the most cases of the disorder observed in patients. Electroencephalography (EEG) is the most common diagnostic tool for Epilepsy, by which abnormal electrical activity of the brain can be clearly seen. This paper uses chaos theory and proposes a new analytical mass model for temporal lobe Epilepsy. Chaotic behavior of the model indicates normal model, while its periodic behavior indicate epileptic mode of the brain. The proposed model includes a number of parameters for which a full bifurcation analysis is conducted. This fully characterizes different regimes of the model and allows studying how one can control the parameters to switch between different modes. The proposed model enables to effectively use advance chaos-based mathematical tools to get further insights on the underlying mechanisms of epilepsy. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the dynamical behaviors of a fractional-order predator–prey with Holling type IV functional response and its discretized counterpart. First, we seek the local stability of equilibria for the fractional-order model. Also, the necessary and sufficient conditions of the stability of the discretized model are achieved. Bifurcation types (include transcritical, flip and Neimark–Sacker) and chaos are discussed in the discretized system. Finally, numerical simulations are executed to assure the validity of the obtained theoretical results. [ABSTRACT FROM AUTHOR]

Highlights • A new model of a vibration system with double layer structure is established. • The system vibration modes can be changed from period-doubling bifurcation to chaos. • The parameters are optimized to improve system stability and shrink chaotic vibration. Abstract This study establishes a dynamic model of a new brake system with two-layer structure to explore the mechanism of vibration and noise reduction of a brake pad with new structure. The model is used to analyze the effects of parameters of the double-layer pad on the stability and stick-slip vibration characteristics of the brake system. The stability of the brake system is optimized by brake parameters with respect to the stability diagram of brake pressure under a relatively wide range. System vibration modes can be changed from period-doubling bifurcation to chaos based on the variation of brake pressure and the parameters of double-layer pad via numerical analysis. The chaotic vibration region is optimized in this study using the correlation coefficient, which consists of friction-layer pad mass m b2 and connection stiffness k 2. Results show that the range of chaotic vibration region can be reduced when the friction-layer pad mass and connection stiffness are large. [ABSTRACT FROM AUTHOR]

Abstract We consider a two-dimensional dynamical system modeling the immune response to a target population. We perform a detailed linear stability analysis to investigate possible stability switches induced by the existence of characteristic delay times of the dynamical processes, mainly a delay in the replication of the target population and delays in the stimulated and cooperative immune responses. We show that stability switches of stable periodic cycle solutions can be induced by enforcing appropriated time delays in the target reproduction as well as in the cooperative immune response. The analytical results are supported by the numerical solution of the corresponding set of delayed differential equations, showing bifurcations and quasi-chaotic behavior. We discuss the possible relevance of the present results in tailoring therapeutic strategies of viral infections exhibiting periodic viral load oscillations. Highlights • Time delays in the immune response can lead to stability switches of the stationary state. • Delays in the virus replication and cooperative immune response are shown to induce bifurcations and chaos. • A chronic oscillatory state can be switched to a chronic stable state by properly tuning the response times. [ABSTRACT FROM AUTHOR]

This paper deals with the bifurcation and chaotic dynamic characteristic of a single-machine infinite-bus (SMIB) power system under two kinds of harmonic excitation disturbance, which are induced by the external periodic load and the outer mechanical disturbance. By applying Melnikov's method, the threshold value for the occurrence of chaotic motion is provided. In addition, the chaotic boundary surface is given. The efficiency of the criteria for chaotic motion obtained in this paper is verified by bifurcation diagram, phase portraits, Poincaré section, and frequency spectrum. The results obtained in this paper will provide a better understanding of the nonlinear dynamic behaviors for this class of SMIB power system subjected to two kinds of harmonic excitation components. [ABSTRACT FROM AUTHOR]

Mathematical models can assist to design and understand control strategies for limited resources in Integrated Pest Management (IPM). This paper studies the dynamical behavior of a Filippov predator–prey model with periodic forcing. Firstly, bifurcation analyses are carried out to show that the Filippov predator–prey ecosystem may have very complex dynamics, i.e. the system may have periodic, quasi-periodic, chaotic solutions, as well as period doubling bifurcations. Meanwhile, the model is analyzed theoretically and numerically to understand how resource limitation and periodic forcing affect pest population outbreaks, the intersection between the initial densities (pest and natural enemy populations) and pest control has been discussed. Furthermore, the sliding surface, sliding mode dynamics, the existence and stability of sliding periodic solution of the proposed model and its application in IPM strategy are investigated. Our results show that several hidden factors can adversely affect our control strategy in limited resource and fluctuating environment. Thus, choosing a proper threshold value ET may play a decisive role in pest control, which confirms that IPM is the optimal control strategy. [ABSTRACT FROM AUTHOR]

Not every chaotic system has the particularity of displaying attractors with a fractal structure. That is why strange attractors remain enthralling not only for their fractal structure, but also for their amazing chaotic and multi-scroll dynamics. In this work, we apply the non-local and non-singular kernel operator to a four-dimensional chaotic system with two equilibrium points and show the existence of various types of attractors, including the butterfly type and strange type. Recently, there have been virulent communications related to the validity or not of the index law in fractional differentiation with non-local operators. These discussions resulted in pointing out many important features of the Mittag-Leffler function used as kernel and suitable to describe more complex real world problems. This paper follows the same momentum by pointing out another important feature of the non-local and non-singular kernel operator applied to chaotic models. We solve the model numerically and discuss the bifurcation and period doubling dynamics that eventually lead to chaos (in the form of butterfly attractor). Lastly, we provide related numerical simulations which prove the existence of a chaotic fractal structure (strange attractors). [ABSTRACT FROM AUTHOR]

The ubiquitous occurrence of cluster patterns in nature still lacks a comprehensive understanding. It is known that the dynamics of many such natural systems is captured by ensembles of Stuart-Landau oscillators. Here, we investigate clustering dynamics in a mean-coupled ensemble of such limit-cycle oscillators. In particular, we show how clustering occurs in minimal networks and elaborate how the observed 2-cluster states crowd when increasing the number of oscillators. Using persistence, we discuss how this crowding leads to a continuous transition from balanced cluster states to synchronized solutions via the intermediate unbalanced 2-cluster states. These cascade-like transitions emerge from what we call a cluster singularity. At this codimension-2 point, the bifurcations of all 2-cluster states collapse and the stable balanced cluster state bifurcates into the synchronized solution supercritically. We confirm our results using numerical simulations and discuss how our conclusions apply to spatially extended systems. [ABSTRACT FROM AUTHOR]

Since the neurologists Hindmarsh and Rose improved the Hodgkin-Huxley model to provide a better understanding on the diversity of neural response, features like pole of attraction unfolding complex bifurcation for the membrane potential was still a mystery. This work explores the possible existence of chaotic poles of attraction in the dynamics of Hindmarsh-Rose neurons with an external current input. Combining with fractional differentiation, the model is generalized with the introduction of an additional parameter, the non-integer order of the derivative σ , and solved numerically thanks to the Haar Wavelets. Numerical simulations of the membrane potential dynamics show that in the standard case where the control parameter σ = 1 , the nerve cell's behavior seems irregular with a pole of attraction generating a limit cycle. This irregularity accentuates as σ decreases (σ = 0.9 and σ = 0.85) with the pole of attraction becoming chaotic. [ABSTRACT FROM AUTHOR]

We study qualitative behavior of a modified prey–predator model by introducing density-dependent per capita growth rates and a Holling type II functional response. Positivity of solutions, boundedness and local asymptotic stability of equilibria were investigated for continuous type of the prey–predator system. In order to discuss the rich dynamics of the proposed model, a piecewise constant argument was implemented to obtain a discrete counterpart of the continuous system. Moreover, in the case of a discrete-time prey–predator model, the boundedness of solutions and local asymptotic stability of equilibria were investigated. With the help of the center manifold theorem and bifurcation theory, we investigated whether a discrete-time model undergoes period-doubling and Neimark–Sacker bifurcation at its positive steady-state. Finally, two novel generalized hybrid feedback control methods are presented for chaos control under the influence of period-doubling and Neimark–Sacker bifurcations. In order to illustrate the effectiveness of the proposed control strategies, numerical simulations are presented. [ABSTRACT FROM AUTHOR]

This paper presents a new four-dimensional chaotic system with three nonlinearities and two equilibria. The most striking feature of the new system is that it has different types of asymmetric coexisting attractors. Simulation experiments are used to study the complex dynamic behaviors of the system. The chaos, period-doubling bifurcation, coexisting attractors with respect to system parameters and initial values are found in the system. It shows that the system has coexisting chaotic attractors, coexisting periodic attractors, coexisting chaotic and periodic attractors. The electronic circuit is applied to implement the chaotic attractor and coexisting attractors for studying the physical significance of the system. In addition, we consider the synchronization of the system by using the impulsive control method. Some synchronization criteria are established via theoretical analysis and simulation example. [ABSTRACT FROM AUTHOR]

The paper investigates the complex nonlinear behavior of a fractional order four dimension power system (FOFDPS). The discrete mathematical model of the FOFDPS is derived and presented. The equilibrium points along with the Eigen values of commensurate and incommensurate FOFDPS are presented. The existence of chaotic oscillations are supported by a positive Lyapunov exponent. Bifurcation plots are derived for both parameters and fractional orders to show the impact of the same on the dynamic behavior of FOFDPS. Having shown the existence of such complex behaviors in the FOFDPS, we present an adaptive fractional order sliding mode control (FOASMC) to suppress the chaotic oscillations. Numerical results are presented to support the theoretical results. [ABSTRACT FROM AUTHOR]

In this research, nonlinear dynamics and characteristics of a micro–plate system under electrostatic forces on both sides are studied. A novel model, which takes micro-scale effect and damage effect into account, is established on the basis of the Talreja's tensor valued internal state damage model and modified couple stress theory. According to Hamilton principle, the dynamic governing equations of the size-dependent micro–plate are derived by variational method and solved via Galerkin method and the fourth order Runge-Kutta method. The effects of damage variable and material length scale parameter on bifurcation and chaos of the micro–plate system are presented with numerical simulations using the bifurcation diagram, Poincare map. Results provide a theoretical basis for the design of dynamic stability of electrically actuated micro- structures. [ABSTRACT FROM AUTHOR]

Designing new chaotic system with specific features is an interesting field in nonlinear dynamics. In this paper, some new chaotic systems with cyclic symmetry are proposed. In order to understand the overall behavior of such systems, the dynamical analyses such as stability analysis, bifurcation and Lyapunov exponent analysis are done. The accurate examination of bifurcation plot represents that these systems are multistable which makes them more interesting. Also, the basin of attraction of these systems is investigated to detect the type of attractors of these systems which are self-excited. Finally, the circuit implementation is carried out to show their feasibility. [ABSTRACT FROM AUTHOR]

In this work, we extend further the analytical study of complex dynamics exist in two coupled logistic maps. New results about the occurrence of various types of bifurcation in the system, including flip bifurcation, pitchfork bifurcation and Neimark–Sacker bifurcation are presented. To the best of authors’ knowledge, the presence of chaotic dynamics in system’s behavior has been investigated and proved analytically via Marotto’s approach for first time. Numerical simulations are carried out in order to verify theoretical results. Furthermore, chaos based encryption algorithm for images is presented as an application for the coupled logistic maps. Different scenarios of attacks are considered to demonstrate its immunity and effectiveness against the possible attacks. Finally, a circuit realization for the coupled logistic maps is proposed and utilized in a suggested real time text encryption system. [ABSTRACT FROM AUTHOR]

The stability and bifurcation of a flexible rod-fastening rotor bearing system with a transverse open crack in a fastening rod are investigated. The nonlinear dynamic model of a cracked rod-fastening rotor system is established based on the finite element method. A methodology is introduced where shooting method, path-following technique, and Floquet theory are combined for determining the periodic solutions and stability margins of the system. The effects of crack depth and mass eccentricities on the system are studied by numerical simulations. Results show the system stability will reduce due to the presence of crack, two saddlebacks occur on the periodic-doubling borderline whose bottom location corresponds to the two resonant peak of bearing node, and effects of the crack and mass eccentricity play a dominant position in different conditions respectively. Comparisons between the cracked rotor system and the intact ones referred in the literature indicate that some special characteristics of cracked rod-fastening rotor system in motion orbits and frequency components can be used to detect the presence of crack and its depth. [ABSTRACT FROM AUTHOR]

Natural convection in a top-open cylindrical cavity heated from the cavity bottom was simulated and analysed for a range of Rayleigh numbers, Ra = 100–106. A succession of bifurcations from steady to chaotic plumes, with increasing Rayleigh numbers, was observed in the three-dimensional simulation results. At Ra = 3.6 × 103, a symmetrical steady plume switched to becoming an asymmetric steady plume with a pitchfork bifurcation, owing to the symmetry break. When the Rayleigh number increased to 8.6 × 104, a periodic puffing flow appeared after a Hopf bifurcation. It was found that the Hopf bifurcation was followed by a cascade of period-doubling bifurcations, then a quasi-periodicity bifurcation, and a bifurcation to chaos for plumes from an open cylinder heated from underneath. The unsteady flow was further analysed using power spectral densities, attractors, and the largest Lyapunov exponents. In addition, the different scaling relationships within different regimes were attained, based on the Rayleigh number. [ABSTRACT FROM AUTHOR]