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In this paper, a size-structured population model is studied. Choosing the coefficient of birth function as the varying parameter, we prove the existence of Hopf bifurcation and discuss the bifurcation properties, such as the direction of Hopf bifurcation and the stability of bifurcated periodic solutions. The methods used in this paper include Hopf bifurcation theorem, center manifold theorem and normal form theory for the abstract Cauchy problems in a nondense domain. Numerical simulations are finally carried out to show the theoretical results. [ABSTRACT FROM AUTHOR]

This paper aims to improve the performance of the piezoelectric buckled beam under low vibration environment using the noncontact magnetic modulation method. Based on the bi-stable buckling beam structure, the magnetic force is introduced to capture more energy. In order to investigate the influence of magnetic force in the process of vibration, the dynamic response of the harvester is analyzed under different magnetic force through numerical simulation and experiment. It is found that the magnetic force has a softening effect on the structure, namely, it could reduce the stiffness of the buckled beam. Therefore, the energy harvester could realize large-amplitude vibration under low-amplitude or low-frequency vibration with the help of magnetic force. The experimental results show that the harvester can realize inter-well vibration only when the vibration acceleration is 3.5 g and the frequency is 15 Hz without the magnetic force. The harvester only needs 2.5 g acceleration or 10 Hz vibration frequency to realize the large-amplitude vibration. While in the case of 12 mm magnetic gap. After the magnetic force is introduced in the harvester, the voltage output under 2.5 g acceleration is increased from 1 to 4 V, and the voltage output at 10 Hz vibration frequency is increased from 0.2 to 2 V. Therefore, the proposed magnetically tuned bi-stable energy harvester can better operate in low frequency and low amplitude environments. [ABSTRACT FROM AUTHOR]

Lag synchronization is a special synchronization manner and has wide applications. For community network, in view of the differences among communities, the synchronization lags in different communities may be nonidentical. This paper investigates the cluster lag synchronization in fractional-order community networks with nondelay and delay coupling. The node dynamics in different communities are nonidentical and even have nonidentical dimensions. Based on the Lyapunov stability theory, effective feedback controllers are designed for achieving cluster lag synchronization and several synchronization criteria are derived. Finally, numerical simulations are provided to demonstrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

A stochastic susceptible–infected–recovered–infected (SIRI) epidemic model with relapse and reinfection is established in this paper. First, we prove that the solution to the epidemic model is unique and globally positive. Next, we determine some sufficient conditions for the extinction of the disease when ℛ0s < 1 and for the persistence in mean in the case of ℛ0s̄ > 1. Furthermore, we prove the existence of at least one ergodic stationary distribution of the stochastic model if ℛ0s̄ > 1. Additionally, by solving the corresponding three-dimensional Fokker–Planck equation, it is theoretically shown that the epidemic model has a log-normal probability density function when ℛ0s̄ > 1, then we obtain the exact expression of density function of the stationary distribution. Finally, we give some numerical simulations to support our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, a two-patch model with additive Allee effect, nonlinear dispersal and commensalism is proposed and studied. The stability of equilibria and the existence of saddle-node bifurcation, transcritical bifurcation are discussed. Through qualitative analysis of the model, we know that the persistence and the extinction of population are influenced by the Allee effect, dispersal and commensalism. Combining with numerical simulation, the study shows that the total population density will increase when the Allee effect constant a increases or m decreases. In addition to suppress the Allee effect, nonlinear dispersal and commensalism are crucial to the survival of the species in the two patches. [ABSTRACT FROM AUTHOR]

The cognitive abilities of animals, such as memory, have a significant impact on their movement in space. In this paper, we consider a radio-dependent model with memory-based diffusion under the conditions of Neumann boundary. The stability of a positive equilibrium and the existence of the Turing–Hopf bifurcation induced by memory diffusion and memory delay are carried out in details. Notably, our findings indicate that with a relatively short average memory period, the large memory diffusion can stabilize an otherwise unstable equilibrium. In addition, the third-order truncated normal form for the Turing–Hopf bifurcation restricted to the central manifold is derived, which can reveal the generation of some steady-state and time-periodic solutions with spatial heterogeneity. The coefficients within the normal form are systematically determined through matrix operations, and these results can also be applied to other models with memory diffusion. Ultimately, leveraging the theoretical findings, we elucidated the intricate spatial-temporal dynamics and their associated parameter scopes caused by Turing–Hopf bifurcation through numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, a fast L1 formula on tanh meshes is proposed for time fractional Burgers equations with Caputo fractional derivative. The solvability, boundness and convergence of the numerical scheme are rigorously established. Several numerical experiments are provided to support the theoretical results. The results of the experiments showed that the proposed numerical method cannot only effectively deal with the weak singularity of the problem near t = 0, but also significantly reduce the computational complexity of numerical simulation. [ABSTRACT FROM AUTHOR]

In this paper, we propose an epidemic model of SIR type with ratio-dependent impulse control and Beddington–DeAngelis (B–D) incidence. According to the magnitude of the basic reproductive number ℛ 0 and the relation of the endemic equilibrium (S ∗ , I ∗) and the ratio threshold h , dynamical analysis of the controlled system is conducted. Under the control strategy, if ℛ 0 ≤ 1 , the solutions converge to the disease-free equilibrium. If ℛ 0 > 1 and I ∗ S ∗ > h , the impulsive system has periodic solution that is orbitally asymptotically stable, and order- k   (k > 2) periodic solution does not exist. Furthermore, if ℛ 0 > 1 and I ∗ S ∗ < h , the solution converges either to the endemic equilibrium or to a periodic solution, which is proved to be determined by the initial value. Finally, numerical simulations are performed to demonstrate the theoretical results. [ABSTRACT FROM AUTHOR]

The principle of minimum differentiation stated by Hotelling in his pioneer paper was proved to be invalid 50 years later, since there is a region where the players are so close that Nash equilibrium does not exist. Some authors have contributed with amendments to the original game in the aim of ensuring the existence of Nash equilibrium independently of the location of the players. However, this work analyzes the less frequently studied case of the Hotelling game with close players under different implementations of the game, considering elastic and inelastic demand (conventional Hotelling game, the Hotelling game with reservation cost and Hotelling-Smithies game). The study is supported by means of numerical simulation of the game. [ABSTRACT FROM AUTHOR]

In this paper, we transform a modified Leslie–Gower predator–prey system into the corresponding fast–slow version by assuming that prey reproduces much faster than predator, and then perform a complete analysis about its dynamics. More specifically, we find the necessary and sufficient conditions of the exact number (zero, one or two) of positive equilibria of the slow–fast system and its (or their) location, and then we further fully determine its (or their) dynamics under explicit conditions. Besides, by converting the slow–fast system into its slow–fast normal form, we are able to characterize its rich dynamics completely, including relaxation oscillation, singular Hopf bifurcation, canard explosion, homoclinic orbits, heteroclinic orbits and global attraction of equilibrium. Moreover, the sufficient conditions to guarantee these various rich dynamics are explicitly given, including the explicit conditions to determine whether singular Hopf bifurcation is supercritical or subcritical, which generally cannot be explicitly derived in the existing literatures. Additionally, the cyclicity of diverse canard cycles is found under explicit conditions. Of particular interest is that we show the existence and uniqueness of one canard cycle without head whose cyclicity is at most two under explicit parameters conditions. Our results complement and enrich the previous work (relaxation oscillation, and global attraction of a boundary equilibrium) about this fast–slow system. We also employ numerical simulations to illustrate our theoretical analysis. [ABSTRACT FROM AUTHOR]

This paper addresses the tracking control challenge in the diving motion system of a specific class of autonomous underwater vehicles (AUVs) characterized by a torpedo-like shape. A decoupled and reduced-order three degrees-of-freedom linearized diving motion model is employed for depth position control. A control law is synthesized using the immersion and invariance (I&I) technique to achieve the control objectives. The primary aim is to attain tracking by immersing a stable, lower-order target (second-order) dynamic system into a three-dimensional manifold, upon which the closed-loop system evolves. We address the regulation problem as a specialized instance of the tracking problem, with the reference input set as a predetermined known depth that requires regulation. The efficacy of the proposed control law is evaluated through simulation studies involving various scenarios. Robustness tests are conducted to assess the control law’s performance under modeling uncertainties and underwater disturbances. The computer simulation employs an AUV named MAYA, utilizing experimentally validated diving motion parameters. A comparative analysis is performed between the proposed control law and other benchmark controllers to gauge its performance. Additionally, the effectiveness of the proposed control law is confirmed by validating its application to the nonlinear model of the diving motion system. [ABSTRACT FROM AUTHOR]

In this paper, we study numerically the dynamics of opinion formation under the influence of mass media using the q-voter model on a Barabasi–Albert network. We investigate the scenario where a voter adopts the mass media’s opinion with a probability p when there is no unanimity among a group of q agents. Through numerical simulation, we identify a critical probability threshold, pt, at which the system consistently reaches complete consensus. This threshold probability pt decreases as the group size q increases, following a power-law relation pt∝qγ with γ≈−1.187. Additionally, we analyze the system’s relaxation time, the time required to reach a complete consensus state. This relaxation time increases with the population size N, following a power-law τ∝Nν, where ν≈1.093. Conversely, an increase in the probability p results in a decrease in relaxation time following a power-law relationship τ∝pδ, with δ≈−0.596. The value of the exponent ν is similar to the exponents obtained in the voter and q-voter models across various network topologies. [ABSTRACT FROM AUTHOR]

This paper focuses on synchronization control of the fractional-order unified chaotic system. First, the stability of equilibria is analyzed by the Routh–Hurwitz criteria. Then, three different controllers are designed to achieve chaos synchronization of the drive-response unified system. Further, the impact of the fractional order on the synchronization performance is illustrated. Numerical simulations are carried out to verify the feasibility of theoretical analysis. [ABSTRACT FROM AUTHOR]

The aim of this paper is to investigate the ventilated cavitating flow behavior, through experimental and numerical methods. The experiments are performed for a test model placed in a water tunnel and a high-speed camera is used to image the formation and collapse of the supercavity. For the numerical simulations, Ansys CFX commercial software is employed to solve the Reynolds-averaged Navier–Stokes (RANS) equations and additional transport equation for the liquid volume fraction in the unsteady condition. Both the experimental observation and numerical prediction show a hysteresis behavior for ventilated supercavity in which the value of the air entrainment coefficient required to maintain the supercavity in the formation process is less than the amount required to form it. The good agreement observed between the numerical prediction and experimental data, revealed the accuracy and capability of the numerical scheme. Also, the numerical simulation shows that the variations in the supercavity length, in addition to the air entrainment, are a function of the air leakage regime from the closure region of supercavity. [ABSTRACT FROM AUTHOR]

In this paper, we consider a Hepatitis C model characterized by acute and chronic infections, treatment as a health-protective measure for the chronically infected is proposed, and its effect on the population is further highlighted. The model is perturbed by white noise and we incorporate Lévy jumps as means to depict abrupt fluctuations. We demonstrate the solution’s existence and uniqueness and deduce adequate criteria for the disease’s extinction and persistence. The importance of treatment as a protective strategy is manifested in its ability to eradicate or mitigate the propagation of the disease. We present numerical simulations to demonstrate the theoretical findings we have obtained. [ABSTRACT FROM AUTHOR]

This paper investigates the synchronizability of multi-layer small-world dynamical networks and discusses the significant factors affecting the synchronizability. First, we introduce the network model of multi-layer small-world dynamical networks with one-to-one connections in the inter-layer connections and each layer has the same topology. Second, we consider the topological parameters including adding probability, intra-layer coupling strength, inter-layer coupling strength, number of nodes per layer, initial node degree, and number of network layers which will influence the network’s synchronizability. Third, we adopt the master stability function method and numerical simulations to analyze the synchronizability of the network. We also examine how the topological parameters influence the synchronizability of multi-layer small-world dynamical networks and the relationships among these parameters. Finally, synchronization control experiments are conducted to verify our results. As a result, we find that only increasing the number of nodes per layer will weaken the synchronizability of multi-layer small-world dynamical networks, while increasing other topological parameters will enhance the synchronizability. The current findings enable us to gain a deeper understanding of the synchronization behavior and characteristics of multi-layer small-world dynamical networks. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the propagation dynamics of a nonlocal dispersal predator–prey model with one predator and two preys. Accurately, we mainly study the invading phenomenon of an alien predator to the habitat of two aborigine preys, which is depicted by traveling waves connecting the predator-free state to the co-existence state. We characterize the minimal wave speed of this invading process based on an application of Schauder’s fixed point theorem with the help of generalized upper-lower solutions and the Lyapunov argument. Particularly, the discussion of traveling waves with critical wave speed is more involved due to the effect of nonlocal dispersal. Finally, a numerical simulation is given to present the traveling waves and shows the differences between non-local and local dispersals. [ABSTRACT FROM AUTHOR]

In this paper, we study a network-based SIR epidemic model with a saturated treatment function in which a parameter α is introduced to measure the extent of the effect of the infected being delayed for treatment. Our aim is to present a global analysis and to investigate how the parameter α affects the spreading of diseases. Our main results are as follows: (1) In the case of the threshold value R 0 < 1 , there exist two values of α : α c and α 0 , such that the disease-free equilibrium is globally asymptotically stable when α ≤ α c and multiple endemic equilibria exist when α ≥ α 0 . This means that the parameter α has an essential influence on the spreading of the disease. (2) In the case of the threshold value R 0 > 1 , if the model has only one endemic equilibrium, then the unique endemic equilibrium is globally attractive. In this case, it is also proved that if α ≤ α c , then the endemic equilibrium has only one, so is globally attractive. In addition, numerical simulation is performed to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, an SIRS model with age structure is proposed for recurrent infectious diseases by incorporating infectious delay and temporary immunity delay. Analysis shows that the disease will eventually disappear when the basic reproduction number ℛ 0 < 1. No matter how the infection delay τ 1 changes, as long as the temporary immunity loss delay τ 2 = 0 , the disease transmission will only be endemic and there will be no periodic oscillations when ℛ 0 > 1. Moreover, the stability and Hopf bifurcation will appear as τ 2 increases from zero. It indicates that the duration of temporary immunity can affect the form of disease transmission within the population. Our numerical simulations verified the correctness of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we present a novel two-dimensional discrete memristor map that is based on a discrete memristor model and a sine–arcsine one-dimensional map. First, an analysis is conducted on the memristor model to understand its characteristics. Then, the model is coupled with the sine–arcsine one-dimensional map to achieve the two-dimensional discrete memristor map. Our investigation reveals the presence of coexisting attractors and hyperchaotic attractors as the bifurcation parameters vary. Numerical simulations show that the discrete memristors effectively enhance the complexity of chaos in the sine–arcsine map. Furthermore, a digital circuit is designed to experimentally verify the new chaotic system. The research results can enrich the theoretical analysis and circuit implementation of chaos. [ABSTRACT FROM AUTHOR]

Over the past years, we have exploited the bistability features that are commonly found in many individual sensors to develop a network-based [Acebrón et al., 2003; Bulsara et al., 2004; In et al., 2003a; In et al., 2003b; In et al., 2005; In et al., 2006; In et al., 2012; Palacios et al., 2005] approach to modeling, designing, and fabricating extremely sensitive magnetic- and electric-field sensors capable of resolving field changes as low as 150 pT and 100 fAmps, respectively. Higher sensitivity is achieved by exploiting the symmetry of the network to create infinite-period bifurcations that render the ensuing oscillations highly sensitive to symmetry-breaking effects from external signals. In this paper, we study the effects of noise on the response of a network-based electric-field sensor as well as the effects of parameter mismatch, which appear naturally due to material imperfections and noise. The results show that Signal-to-Noise Ratio (SNR) increases sharply near the onset of the infinite-period bifurcation, and they increase further as the coupling strength in the network increases while passing the threshold that leads to oscillatory behavior. Overall, the SNR indicates that the negative effects of highly contaminated signals are well-mitigated by the sensitivity response of the system. In addition, computer simulations show the network-based system to be robust enough to mismatches in system parameters, while the deviations from the nominal parameter values form regions where the oscillations persist. Noise has a smoothing effect over the boundaries of these regions. [ABSTRACT FROM AUTHOR]

In this paper, we study a gang territorial model consisting of two parabolic and two ordinary differential equations, where a taxis-type mechanism models that the two rivaling gangs are repelled by each other's graffiti. Our main analytical finding shows the existence of global, bounded classical solutions. By making use of quantitative global estimates, we prove that these solutions converge to homogeneous steady states if the initial data are sufficiently small. Moreover, we perform numerical experiments which show that for different choices of parameters, the system may become diffusion- or convection-dominated, where in the former case the solutions converge toward constant steady states while in the latter case nontrivial asymptotic behavior such as segregation is observed. In order to perform these experiments, we apply a nonlinear finite element flux-corrected transport method (FEM-FCT) which is positivity-preserving. Then we treat the nonlinearities in both the system and the proposed nonlinear scheme simultaneously using fixed-point iteration. [ABSTRACT FROM AUTHOR]

In this paper, a delayed cytokine-enhanced viral infection model incorporating nonlinear incidence and immune response is proposed and studied. The global stabilities of the equilibria of the model are characterized by constructing suitable Lyapunov functionals. The existence and properties of local Hopf bifurcation are discussed by regarding the immunity delay as the bifurcation parameter. Moreover, the global existence of Hopf bifurcation has been proved by regarding the immune delay as the bifurcation parameter. Numerical simulations are carried out to validate the obtained results. The results show that ignoring the cytokine-enhanced effect makes the infection risk underevaluated. The simulations show that increasing the immune delay destabilizes the model and generates a Hopf bifurcation and stability switches occurs. Moreover, it shows that immune delay may dominate the intracellular delays in such a viral infection model which means that the immune system of the host itself is complicated during virus infection. [ABSTRACT FROM AUTHOR]

The TPMS lattice structure is widely utilized in the military UAV, and effectively striking the TPMS structure holds significant reference value in bullet design. This paper conducts a numerical simulation to study the penetration performance of exponential curve bullets with varying power exponents on the TPMS structures of Gyroid and Diamond. MATLAB is employed to design the TPMS lattice structure, and ABAQUS is used for numerical simulation. The results indicate that the velocity reduction rate of the bullet initially increases and then decreases with an increase in power exponent. Moreover, a larger power exponent leads to a smaller residual velocity and kinetic energy of the bullet. Different cell structures have a substantial impact on residual kinetic energy, with the Gyroid structure exhibiting significantly greater residual kinetic energy compared to the Diamond structure, resulting in an average kinetic energy difference of 15.429J. The research shows that the curve of the arc part of the warhead has a great influence on the penetration performance. When designing the bullet used to hit the military UAV, the warhead with a large curvature change within a certain range can be considered. [ABSTRACT FROM AUTHOR]

As a kind of classical fractal network models, Sierpinski Gasket and its extended network models have attracted the attention of many scholars because of their many applications in real-world networks. Based on the classical Sierpinski Gasket, this paper proposes a joint Sierpinski Gasket model, which can be used not only to study the topology and dynamic properties of Sierpinski Gasket itself, but also to study the Sierpinski Gasket under special conditions, such as the residual Sierpinski Gasket after damage. Since the mean time to absorption (MTA) on the network is a basic dynamic property related to the random walk, in this paper, we study the expression of MTA on the proposed general joint Sierpinski Gasket model, and find that the MTA is determined by the number of iterations g and two variables determined by the mode variable S , which can be solved by matrix algorithm. Therefore, using the expression of MTA on the general joint Sierpinski Gasket model, we calculate the analytical expressions of the MTA on a general example of the joint Sierpinski Gasket model and three Sierpinski Gaskets with varying degrees of damage and do the corresponding numerical simulation to verify the correctness of the conclusion. [ABSTRACT FROM AUTHOR]

The bifurcation phenomenon generated in neurons is considered to be the cause of many neurological diseases, thus, lots of investigators have been dedicated to bifurcation control, but most of them only focus on the integer-order neuronal models and control methods. Recently, increasing number of research works have shown that the differential equations of fractional-order are more appropriate for description of the electrical properties of certain nerve cell membranes. In this paper, we employ a fractional-order washout filter to realize bifurcation control for fractional-order Morris–Lecar neuronal model. Computer simulation verifies the effectiveness and improved performance of the proposed method than the integer-order washout filter. In addition, the analysis of the fractional-order controller's impacts on the model is also presented. [ABSTRACT FROM AUTHOR]

This paper derives a new fractional Fokas system with the aid of the local fractional derivative. A novel technology named the extended rational fractal sine–cosine method is presented for the first time ever to develop the abundant traveling wave solutions. Two families (six sets) of the traveling wave solutions on Cantor set are successfully constructed. The dynamic behaviors of the solutions on Cantor sets are provided via numerical simulations. The obtained results in this work strongly prove that the proposed approach is simple but effective, which is expected to shed a new light on the study of the traveling wave theory of the local fractional equations. [ABSTRACT FROM AUTHOR]

This paper carries out numerical simulations of highly dispersive optical solitons with differential group delay having quadratic-cubic law of nonlinearity. The Laplace–Adomian decomposition scheme is implemented to visualize the soliton propagation dynamics. Both bright and dark solitons are addressed. The error measure for these numerical approximations is impressively low as presented. [ABSTRACT FROM AUTHOR]

For high-rise buildings subjected to typhoon or earthquake actions, the excitations are likely non-stationary, which inevitably violates the stationary assumption that is generally adopted by conventional modal identification methods. Under such a condition, conventional modal identification methods may not be applicable, and their performances need to be evaluated. To this end, the performances of seven widely used modal identification algorithms for structural modal estimation under non-stationary excitations are evaluated via a numerical simulation study. Then, three methods with good performance are selected to evaluate their applicability and accuracy for field measurements involving non-stationary excitations. From the comparative study, a time–frequency domain method with the best performance among these seven methods is employed to investigate the structural dynamic properties of a 509-m-tall skyscraper under typhoon and earthquake excitations. Based on the reliable modal estimates, the relationships between the modal properties with response amplitude and environmental temperature are presented and discussed. This paper aims to identify the effective methods for accurate estimation of structural modal parameters based on non-stationary structural responses and investigate the structural dynamic properties of high-rise buildings under typhoon and earthquake excitations. [ABSTRACT FROM AUTHOR]

This paper considers the load–deflection behavior of a pyramid-like, shallow lattice structure. It consists of four beams that join at a central apex and when subject to a lateral load, it exhibits a propensity to snap-through: a classical buckling phenomenon. Whether this structural inversion occurs, and the routes by which it happens, depends sensitively on geometry. Given the often sudden nature of the instability, the behavior is also examined within a dynamics context. The outcome of numerical simulations are favorably compared with experimental data extracted from the testing of three-dimensional (3D)-printed specimens. The key contributions of this paper are that despite the continuous nature of the physical system, its behavior (transient and equilibria) can be adequately described using a discrete model, and the paper also illustrates the utility of 3D-printing in an accessible research context. [ABSTRACT FROM AUTHOR]

In this research work, we proposed a modern structured packing (SP) with perforated sheets with a specific surface area of 860 m 2 / m 3 , which was determined using numerical techniques. This work aims to evaluate the major characteristics of PACK-860 for instance, height equivalent to a theoretical plate (HETP), dry pressure drop (DPD) and wet pressure drop (WPD). Additionally, the flow construction was defined for specific packing via computational simulation. To evaluate the value of HETP, DPD and WPD, the three-dimensional (3D) computational fluid dynamics (CFD) simulation with the Eulerian–Eulerian (EE) multi-phase method applied in this paper. According to the findings of this research, the performance of the mass transfer (MT), WPD and DPD was enhanced with the perforated-on sheets of packing. Based on the observation, numerical results are consistent well with the theoretical data which reveals the consistency of CFD tools for modeling methods to separation applications. [ABSTRACT FROM AUTHOR]

In this paper, we consider a modified Lasslie–Gower-type predator–prey model with the effect of hunting cooperation and favorable additional food for predator. We establish the conditions of positivity, boundedness, and permanence of solutions of the proposed model. Along with the trivial, predator free, prey free equilibrium points the system contains at most two coexistence equilibrium points. The system experiences the transcritical, saddle-node, Hopf, cusp, Bautin, and Bogdanov–Takens bifurcation depending on the model parameters. All the theoretical analyses are verified using numerical simulations. It is numerically established that the cooperation and extra food have high impact on the model dynamics. [ABSTRACT FROM AUTHOR]

This paper studies the dynamics of a class of host-parasitoid models with host refuge and the strong Allee effect upon the host population. Without the parasitoid population, the Beverton–Holt equation governs the host population. The general probability function describes the portion of the hosts that are safe from parasitism. The existence and local behavior of solutions around the equilibrium points are discussed. We conclude that the extinction equilibrium will always have its basin of attraction which implies that the addition of the host refuge will not save populations from extinction. By taking the host intrinsic growth rate as the bifurcation parameter, the existence of the Neimark–Sacker bifurcation can be shown. Finally, we present numerical simulations to support our theoretical findings. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a deterministic mathematical model of Marburg–Monkeypox virus co-infection transmission under the Caputo fractional-order derivative. We discussed the dynamics behavior of the model and carried out qualitative and quantitative analysis, including the positivity–boundedness of solution, and the basic reproduction number ℜ o . In addition, the Banach and Schauder-type fixed point theorem is utilized to explore the existence–uniqueness of the solution in the suggested model and the proposed model stability under the Ulam–Hyers condition is demonstrated. In numerical simulation, the Predictor–Corrector method is used to determine the numerical solutions. According to the numerical result, increasing the rate of quarantine and detecting unknown Marburg virus, will be the most effective control intervention to reduce Marburg and Monkeypox virus transmission in the population. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study the dynamical behaviors of a piecewise smooth predator–prey model with predator harvesting. We consider a harvesting strategy that allows constant catches if the population size is above a certain threshold value (to obtain predictable yield) and no catches if the population size is below the threshold (to protect the population). It is shown that boundary equilibrium bifurcation and sliding–grazing bifurcation can happen as the threshold value varies. We provide analytical analysis to prove the existence of sliding limit cycles and sliding homoclinic cycles, the coexistence of them with standard limit cycles. Some numerical simulations are given to demonstrate our results. [ABSTRACT FROM AUTHOR]

In this paper, we study a stochastic predator–prey model with Beddington–DeAngelis functional response and time-periodic coefficients. By analyzing the stability of the solution on the boundary and some stochastic estimates, the threshold conditions for the time-average persistence in probability and extinction of each population are established. Furthermore, the existence of a unique periodic measure of the model is also presented under the condition of the time-average persistence in probability of the model. Several numerical simulations are given to verify the effectiveness of the theoretical results and to illustrate the effects of the white noises on the persistence and periodic measure of the model. [ABSTRACT FROM AUTHOR]

In this paper, we study the spatiotemporal dynamics in a diffusive cell polarization model with source and loss terms under zero flux boundary conditions. Firstly, we investigate the stability of the positive equilibrium and the existence of Hopf bifurcation for the system without diffusion. Secondly, Turing instability and Turing bifurcation near the positive constant equilibrium are discussed for the diffusive system. Thirdly, the normal forms on the center manifold are given to determine the properties of Turing and Hopf bifurcations. Finally, numerical simulations are performed to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

This paper deals with the design of a CPU cooling system using a novel numerical modelling approach based on automatic calculation in a commercial software. A research object is an aluminium CPU heat sink with a thermal design power of 50 W with a new fin design. A numerical model of the cooling process has been developed, and the heat sink efficiency has been investigated. The main goal of optimization was to get the minimum temperature of the CPU processor at the minimum mass of the heat sink. The comparative analysis of the results that obtained via three methods (screening, adaptive multiple-objective, multi-objective genetic algorithm) was performed. This analysis showed that screening was the least time-consuming method, but it did not provide the required solution. Adaptive multiple-objective and multi-objective genetic algorithm solutions show similar results but significantly differ in time. It was established that the adaptive multiple-objective method is the best method for the heat sink optimization task. At the determined optimal design parameter, the CPU temperature is in the range 304–307 K, while the mass was 81–87 g. In comparison, the heat sink mass before optimization of the design parameters was 93 g at the CPU temperature of 309–311 K. [ABSTRACT FROM AUTHOR]

This paper investigates the dynamics of a model of two chemostats connected by Fickian diffusion with bounded random fluctuations. We prove the existence and uniqueness of non-negative global solution as well as the existence of compact absorbing and attracting sets for the solutions of the corresponding random system. After that, we study the internal structure of the attracting set to obtain more detailed information about the long-time behavior of the state variables. In such a way, we provide conditions under which the extinction of the species cannot be avoided and conditions to ensure the persistence of the species, which is often the main goal pursued by practitioners. In addition, we illustrate the theoretical results with several numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, we propose a Leslie–Gower predator–prey model with strong Allee effect on prey and fear effect on predator. We discuss the existence and local stability of equilibria by making full use of qualitative analytical theory. It is shown that the above system exhibits at most two positive equilibria and it can undergo a series of bifurcation phenomena. We indicate that the dynamical behavior of the model is closely related to the fear effect on predator. In detail, when the fear effect parameter p = p ∗ , the system will undergo degenerate Hopf bifurcation. There exist two limit cycles (the inner is stable and the outer is unstable). However, when p = p ∗ , the system will undergo degenerate Bogdanov–Takens bifurcation. Also, by numerical simulation, we conclude that the stronger the fear effect, the bigger the density of prey species. The above shows that fear effect on predator is beneficial to the persistence of the prey species. Our results can be seen as a complement to previous works [González-Olivares et al., 2011; Pal & Mandal, 2014]. [ABSTRACT FROM AUTHOR]

There is a problem of capacity mismatch between different companies in the current market. In this paper, we propose a dual-channel capacity sharing supply chain consisting of two competing manufacturers (i.e. a capacity seller and a capacity buyer) and one platform. Considering the gap of matching success rates, we investigate whether the buyer and seller can benefit from capacity sharing and how the different matching success rates influence the manufacturers' decisions on spontaneously match through a platform. Through numerical simulation, we find that (1) the seller can always benefit from capacity sharing even when the match fails, while the buyer benefits from capacity sharing only when the capacity constraint is relatively severe; (2) both the buyer and seller prefer to participate through the platform when the platform has a sufficiently high advantage in matching success rates; (3) if the capacity constraint is much severe, the capacity buyer may turn to self-match rather than capacity sharing. Besides, we also study the sustainability of the capacity-sharing system and show how the platform can improve sustainability by forgoing accumulated profits. [ABSTRACT FROM AUTHOR]

In this paper, the synchronization of discrete-time complex dynamical network with dynamic links is investigated. From the angle of large-scale system, if the links and nodes are time-varying, the complex dynamical network may be regarded to be composed of nodes subsystem (NS) and links subsystem (LS). The weighted value of links between nodes can be regarded as the state variables of LS, the above two subsystems are mutually coupled. The two subsystems are modeled mathematically by the state difference equations, especially, the dynamics of LS is modeled as Riccati matrix difference equation without control input. Different from the previous researches, this work concerns simultaneously the dynamics of LS and NS, by which the synchronization of NS is investigated. Associated with the given dynamic reference target for LS, the nodes controller is synthesized to ensure the state synchronization of NS to be achieved with the assistance of the LS. Finally, the numerical simulation is given to illustrate the effectiveness of the proposed theoretical results in this paper. [ABSTRACT FROM AUTHOR]

The dynamics of the tubular chemical reactor with mass recycle was examined. In such a system, temperature and concentrations may oscillate chaotically. This means that state variable values are then unpredictable. In this paper, it has been shown that despite the chaos, the behavior of such a reactor can be predictable. It has been shown that this phenomenon can occur in two cases. The first case concerns intermittent chaos. It has been shown that intermittent outbursts can occur at regular intervals. The second case concerns transient chaos, i.e. a situation when chaos occurs only for a certain period of time, e.g. only during start-up. This phenomenon makes it impossible to predict what will occur in the reactor in the nearest time, but, makes it possible to precisely determine the values of the variables even in the distant future. Both of these phenomena were tested by numerical simulation of the mathematical model of the reactor. [ABSTRACT FROM AUTHOR]

In classical artificial intelligence and machine learning fields, the aim is to teach a certain program to find the most convenient and efficient way of solving a particular problem. However, these approaches are not suitable for simulating the evolution of human intelligence, since intelligence is a dynamically changing, volatile behavior, which greatly depends on the environment an agent is exposed to. In this paper, we present several models of what should be considered, when trying to simulate the evolution of intelligence of agents within a given environment. We explain several types of entropies, and introduce a dominant function model. By unifying these models, we explain how and why our ideas can be formally detailed and implemented using object-oriented technologies. The difference between our approach and that described in other papers also — approaching evolution from the point of view of entropies — is that our approach focuses on a general system, modern implementation solutions, and extended models for each component in the system. [ABSTRACT FROM AUTHOR]

Wind-driven rain (WDR) and its interactions with structures is an important research subject in wind engineering. As bridge spans are becoming longer and longer, the effects of WDR on long-span bridges should be well understood. Therefore, this paper presents a comprehensive numerical simulation study of WDR on a full-scale long-span bridge under extreme conditions. A validation study shows that the predictions of WDR on a bridge section model agree with experimental results, validating the applicability of the WDR simulation approach based on the Eulerian multiphase model. Furthermore, a detailed numerical simulation of WDR on a long-span bridge, North Bridge of Xiazhang Cross-sea Bridge is conducted. The simulation results indicate that although the loads induced by raindrops on the bridge surfaces are very small as compared to the wind loads, extreme rain intensity may occur on some windward surfaces of the bridge. The adopted numerical methods and rain loading models are validated to be an effective tool for WDR simulation for bridges and the results presented in this paper provide useful information for the water-erosion proof design of future long-span bridges. [ABSTRACT FROM AUTHOR]

This paper is a brief introduction to the mathematical tools employed in the modeling and simulation of the interactions of a large number of living entities, and provides a presentation of the papers published in a special issue devoted to this topic. In addition, we bring to the reader’s attention some perspective ideas on possible objectives of future researches. [ABSTRACT FROM AUTHOR]

In this paper, a flux-controlled memristor with linear memductance is proposed. Compared with the memristor with piecewise linear memductance and the memristor with smooth continuous nonlinearity memductance which are widely used in the study of memristive chaotic system, the proposed memristor has simple mathematical model and is easy to implement. Multisim circuit simulation and breadboard experiment are realized, and the memristor can exhibit a pinched hysteresis loop in the voltage-current plane when driven by a periodic voltage. In addition, a new hyper-chaotic system is presented in this paper by adding the proposed memristor into the Lorenz system. The transient chaos and multiple attractors are observed in this memristive system. The dynamical behaviors of the proposed system are analyzed by equilibria, Lyapunov exponents, bifurcation diagram and phase portrait. Finally, an electronic circuit is designed to implement the hyper-chaotic memristive system. [ABSTRACT FROM AUTHOR]

In this paper, a boost converter emulator with a memristive load instead of a resistive load is proposed, and a fractional-order model of the memristive boost converter is created. Firstly, the fractional-order models of the memristor and the memristive boost converter are established respectively, and then based on different switching states, the circuit equations of the fractional-order memristive boost converter operating in continuous conduction mode are derived. Secondly, the dynamic characteristics of the fractional-order system are analyzed by numerical simulations and are compared with the integer-order memristive boost converter. Furthermore, the effects of the memristive load on the system is studied by comparing it to the traditional boost converter with resistive load. The results indicate that the fractional-order memristive boost converter can exhibit rich dynamic behavior by adjusting bifurcation parameters, and the fractional-order circuit system expands the stable working regions of the integer-order circuit system. Meanwhile, the addition of the memristive load significantly widens the normal working regions. Finally, simulations of the fractional-order system circuit based on PSIM further verify the correctness of the theoretical analysis. [ABSTRACT FROM AUTHOR]

An extended Neyman–Pearson detector based on the combination of a traditional matched and wavelet filter in pulsed monostatic radar was proposed in this paper. Its properties were compared with properties of the cell average constant false alarm radar detector in the presence of white noise. The properties of detectors were examined in the receiver operating characteristic curves, parameter space. It consisted of false detection rate and the rate of true positive detected targets. In order to investigate the influence of temperature, the new parameter space was constructed: the temperature versus the rate of true positive detected targets. The traditional Neyman–Pearson detector based on a matched filter was fully operational and superior in the temperature range between 290 K and 350 K. Below this temperature range, its performance is completely degraded. It has been shown that by adding a wavelet filter, it can extend this temperature range between 260 K and 350 K. In the temperature range, where all detectors are fully operational, extended and classic Neyman–Pearson detectors had better performance than constant false alarm radar detector in the receiver operating characteristic curves' parameter space. [ABSTRACT FROM AUTHOR]

In this paper, we study a dual-channel closed-loop supply chain (CLSC) consisting of one manufacturer, one retailer and one third-party firm or platform (3P). The manufacturer wholesales new products through the traditional retail channel and distributes remanufactured products via 3P. We focus on establishing the dynamic Stackelberg game models for nondelayed and delayed cases, respectively. The existence and local stability of Nash equilibrium are examined as well as the complex dynamical behaviors of each model under various scenarios are investigated by numerical simulations, such as stability region, bifurcations, chaos, strange attractors, and so on. Moreover, the impacts of some key parameters on the performance of chain members are analyzed. In addition, the variable feedback control method is utilized to eliminate the system chaos. The results reveal that the high value of the consumer discount perception for remanufactured products and excessively fast price adjustment speed have a destabilization effect on the Nash equilibrium point. In addition, adopting delay decisions by manufacturer does not always make the system more stable because it can exert either positive or negative effect on the system's stability, while an intermediate delay weight is conducive to the system have a higher chance to stay stable. Furthermore, the manufacturer's profits will be declined significantly while the profits of retailer and 3P will be elevated to some extent when the system falls into periodic and chaotic motions, so chaos is not always necessarily detrimental to all the decision makers in the dual-channel CLSC. [ABSTRACT FROM AUTHOR]