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This work investigates a prey–predator model featuring a Holling-type II functional response, in which the fear effect of predation on the prey species, as well as prey refuge, are considered. Specifically, the model assumes that the growth rate of the prey population decreases as a result of the fear of predators. Moreover, the detection of the predator by the prey species is subject to a delay known as the fear response delay, which is incorporated into the model. The paper establishes the preliminary conditions for the solution of the delayed model, including positivity, boundedness and permanence. The paper discusses the existence and stability of equilibrium points in the model. In particular, the paper considers the discrete delay as a bifurcation parameter, demonstrating that the system undergoes Hopf bifurcation at a critical value of the delay parameter. The direction and stability of periodic solutions are determined using central manifold and normal form theory. Additionally, the global stability of the model is established at axial and positive equilibrium points. An extensive numerical simulation is presented to validate the analytical findings, including the continuation of the equilibrium branch for positive equilibrium points. [ABSTRACT FROM AUTHOR]

In this paper, a mathematical model for a solid spherically symmetric vascular tumor growth with nutrient periodic supply and time delays is studied. Compared to the apoptosis process of tumor cells, there is a time delay in the process of tumor cell division. The cells inside the tumor obtain nutrient σ(r,t) through blood vessels, and the tumor attracts blood vessels at a rate proportional to α(t). So, the boundary value condition ∂σ ∂r + α(t)(σ − ψ(t)) = 0,r = R(t),t > 0, holds on the boundary, where the function ψ(t) is the concentration of nutrient externally supplied to the tumor. Considering that the nutrients provided by the outside world are often periodic, the research in this paper assumes that ψ(t) is a periodic function. Sufficient conditions for the global stability of zero steady state are presented. Under certain conditions, we prove that there exists at least one periodic solution to the model. The results are illustrated by computer simulations. [ABSTRACT FROM AUTHOR]

The regularized lattice Boltzmann method (RLBM) has the advantage of improving the accuracy of numerical simulations without increasing the computational overhead. The RLBM usually uses the standard Cartesian grid in numerical simulation. This paper introduces the multi-layer grid technique, the multi-layer grid has different resolutions, which is also more consistent with the physical laws of the flow field. Based on this, a multi-layer grid regularized lattice Boltzmann method (ML-RLBM) for solving complex flow problems is proposed. The proposed method performs local refinement of the grid on the standard Cartesian grid to achieve a multi-layer grid, which can reduce the computational overhead. In order to realize the local grid refinement easily, this paper adopts the center point format to store the multi-layer grid. The ML-RLBM designs a buffer scheme between different layers of grids, which realizes that only spatial interpolation is required at the interface of different layers of grids without temporal interpolation. The numerical results show that the ML-RLBM has excellent numerical accuracy and numerical stability, and it can effectively reduce the computational cost. [ABSTRACT FROM AUTHOR]

In this paper, a new delayed fractional-order model including susceptible migratory birds, infected migratory birds and predators is proposed to discuss the spread of diseases among migratory birds. Fear of predators is considered in the model, as fear can reduce the reproduction rate and disease transmission rate among prey. First, some basic mathematical results of the proposed model are discussed. Then, time delay is regarded as a bifurcation parameter, and the delay-induced bifurcation conditions for such an uncontrolled system are established. A novel periodic pulse feedback controller is proposed to suppress the bifurcation phenomenon. It is found that the control scheme can successfully suppress the bifurcation behavior of the system, and the pulse width can be arbitrarily selected on the premise of ensuring the control effect. Compared with the traditional time-delay feedback controller, the control scheme proposed in this paper has more advantages in practical application, which not only embodies the advantages of low control cost and easy operation but also caters to the periodic changes of the environment. The proposed control scheme, in particular, remains effective even after the system has been disrupted by a constant. Numerical simulation verifies the correctness of the theoretical results. [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, 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, 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]

This paper examines a three-dimensional delayed discrete neural network model analytically and numerically to determine the existence of different types of bifurcations of the involved fixed points. The model exhibits different bifurcations such as pitchforks, flips, Neimark–Sackers, and flip-Neimark–Sackers. The critical coefficients are used to determine the structure of each bifurcation. The curves are calculated and plotted for each bifurcation when the parameters are changed. Further, these bifurcations are theoretically analyzed and numerically verified. From the obtained results, we observed that by drawing the curves associated with each bifurcation, the numerical simulations are consistent with the analytical results. [ABSTRACT FROM AUTHOR]

In this paper, we consider a Leslie–Gower type reaction–diffusion predator–prey system with an increasing functional response. We mainly study the effect of three different types of diffusion on the stability of this system. The main results are as follows: (1) in the absence of prey diffusion, diffusion-driven instability can occur; (2) in the absence of predator diffusion, diffusion-driven instability does not occur and the non-constant stationary solution exists and is unstable; (3) in the presence of both prey diffusion and predator diffusion, the system can occur diffusion-driven instability and Turing patterns. At the same time, we also get the existence conditions of the Hopf bifurcation and the Turing–Hopf bifurcation, along with the normal form for the Turing–Hopf bifurcation. In addition, we conduct numerical simulations for all three cases to support the results of our theoretical analysis. [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]

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 ℛ0 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 ℛ0 ≤ 1, the solutions converge to the disease-free equilibrium. If ℛ0 > 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 ℛ0 > 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 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]

This paper presents the stability and bifurcation of the Hindmarsh–Rose neuronal model with time delay. First, we discuss the existence and stability of the equilibria, revealing that the system can have a maximum of three equilibria which exhibit always stable, always unstable, and stability switching dynamics, depending on the stability of the equilibria when there is no time delay. Furthermore, an explicit formula for the time delay at which Hopf bifurcation occurs is derived, and the direction and stability of the Hopf bifurcation are also given. Finally, numerical simulations are carried out to support our theoretical results. We find that due to the existence of time delay, our system can exhibit many interesting dynamical behaviors depending on the number of equilibria and the increase in time delay. For instance, with increasing time delay, bistability transitions to the coexistence of a periodic solution and a stable equilibrium, followed by the emergence of quasi-periodic motion alongside stable equilibria, and eventually leading to chaotic motion coexisting with a stable equilibrium. [ABSTRACT FROM AUTHOR]

The investigation on vehicle–bridge interaction systems (VBIS) plays an important role in evaluating the performance of bridges and/or vehicles. However, due to the limitations of traditional simulation methods and testing methods, the impact of vehicle jumping (VJ) on the VBIS has never been precisely disclosed. In order to accurately and comprehensively reveal the impact of VJ on the dynamic performance of VBIS, one real-time hybrid simulation method (RHSM) for VBIS considering the impact of VJ (VBIS-VJ) is proposed in this paper. In the proposed method, the vehicle system is chosen as the experimental substructure loaded by servo-hydraulic actuator loading system in real-time, whilst the bridge system is chosen as the numerical substructure numerically simulated in one computer. During the vehicle jumping, the vehicle and bridge vibrate freely respectively, otherwise, the experimental substructure and numerical substructure are synchronized at the coupling points in terms of force equilibrium and deformation compatibility in RHSM for VBIS-VJ. Firstly, the principle and numerical models of RHSM for VBIS-VJ are proposed. Furthermore, numerical simulations of RHSM for VBIS-VJ are conducted for verifying the feasibility of the proposed method. Finally, the influence of jumping position, jumping height, and driving speed on the VBIS is disclosed by hybrid simulations. It is shown that compared with the ever-known investigation methods, the proposed method could economically and accurately disclose the dynamic performance of VBIS-VJ. It is shown from the simulation results that compared with the referenced results, the quantitative errors of the proposed method with quarter vehicle model and half vehicle model are less than 2.5152% and 3.5599% respectively, which prove the effectiveness and accuracy of proposed RHSM for VBIS-VJ. The peak displacement of the bridge at a quarter-span and mid-span exceeds the three-quarters span by about 1.9–2.9 mm. The influence of jumping position of a quarter span and midspan of bridge is much huger than that in the three-quarters span. The dynamic response of bridge increases with the increase the jumping height, but the deformation of the bridge is reduced when the jumping height is more than 0.05 m. Meanwhile, the requirements for experimental loading equipment are acquired through the hybrid simulations, which could be used as a reference for selecting the loading system of the RHSM for VBIS-VJ. [ABSTRACT FROM AUTHOR]

In this paper, we propose a stochastic cholera model that incorporates media coverage and two time delays driven by Lévy noise in order to deeply understand the propagation process of cholera in the real world, generalized nonlinear incidence rates β1(M) and β2(M) are also introduced. First, we discuss the existence and uniqueness of the global positive solution of the stochastic model by using the Lyapunov method. Moreover, the dynamic properties of stochastic solution around the disease-free and endemic equilibria are demonstrated. At last, we present numerical simulation results to reveal how Lévy jumps, time delays and media coverage affect the asymptotic properties of the stochastic model. [ABSTRACT FROM AUTHOR]

This paper proposes a mathematical model to investigate the dynamic behaviors of a modified computer virus model using the Atangana–Baleanu fractional derivative in the Caputo sense, aiming to elucidate the connection between its parameters and network attributes. By introducing a relatively new numerical method, we address the memory-dependent and nonlocal features of the system. The existence and uniqueness of the model’s solution are confirmed. To explore solution trajectories and assess the impact of various input factors on computer virus dynamics, we employ an efficient numerical technique. Our simulations provide insights into the consequences of fractional order, anti-virus measures, asymptotic fraction, damage rate, and removal rate in the system. These findings illuminate the relationships between model parameters, facilitating the design of networks that minimize the risk of virus outbreaks and prevent future cyber threats. By identifying critical factors involved in the progression of viruses, these results enable the development of more effective defense mechanisms. [ABSTRACT FROM AUTHOR]

In this paper, we study the dynamic behaviors and chaos synchronization of the Chen system described by Caputo–Hadamard fractional derivative. First, the existence and uniqueness of a solution to the Chen system with Caputo–Hadamard derivative are proved by qualitative analysis. Further, the stability of equilibria of the considered system is analyzed with the aid of Routh–Hurwitz criteria. Meanwhile, the bifurcation condition of the Caputo–Hadamard Chen system is compared with the integer-order Chen system, where the differences between the two systems are demonstrated numerically. In the study of chaos synchronization of the drive–response Chen systems with Caputo–Hadamard derivative, two control schemes are developed: three nonlinear controllers and single linear controller. The feasibility of two control schemes is verified, and the synchronization performances of these two schemes are compared by numerical simulations. Based on this, the influence of the fractional-order on chaos synchronization performance is illustrated as well. [ABSTRACT FROM AUTHOR]

This paper proposes a two-dimensional modified Leslie–Gower predator–prey model with carry-over effects, fear, prey protection and additional food, including prey harvesting. For this, it assumes the carry-over effect with delay incorporated in the birth rate of the prey population and gestation delay in Leslie–Gower term of a predator, and supposes that the predator consumes the prey according to Holling type II functional response. This dynamical system is split into two groups, namely non-delayed and delayed systems, respectively. In the non-delayed system, first, we discuss positivity, boundedness solutions, and the existence of equilibria, especially finding the coexistence of interior equilibrium points under certain conditions. After that, local and global stabilities are systematically analyzed. In addition, we obtain the conditions of Hopf-bifurcation in terms of the growth rate of prey species, prey protection and preference rate of predator for the non-delayed system. Whereas in the delayed system, both the delays have an essential role in governing the dynamical system discussed in three cases, and each case found the Hopf-bifurcation parameters for which the system changes stability behavior into instability. At last, the numerical simulations have been carried out to verify the theoretical findings. [ABSTRACT FROM AUTHOR]

A mathematical model has been proposed to consider two distinct forms of psychological pressure that arise due to the COVID-19 situation and their impact on individuals' lives, including their mental well-being and happiness. For a more realistic situation, the effect of stochasticity should be taken into account. Hence, our paper mainly investigates the effect of stochastically environmental variability on the transmission dynamics of psychological stress. We obtain two thresholds ℛ s 1 and ℛ s 2 . If ℛ s 1 > 1 , the psychological stress will persist and there will be a unique stationary distribution; whereas if ℛ s 2 < 1 , the extinction of psychological stress is obtained. Moreover, we display the mean first passage time from the initial value to the state of disappearance in order to examine the impact of environmental disturbances; meanwhile, we conduct numerical simulations to illustrate the theoretical findings. [ABSTRACT FROM AUTHOR]

The paper aims to perform numerical simulations of flapping flight using Discrete Vortex Method (DVM) scheme. The scheme is suitable for moderately low Reynolds number (< ∼ 1 0 5) and computationally less expensive as the flow domain doesn't need to be discretized at each time step. Flapping of a one-dimensional (1D) flexible filament in a two-dimensional (2D) inviscid flow is simulated. The effect of bending by varying the wing shape along the spanwise length on aerodynamic performance was studied. It is observed that compared to rigid wings, bending wings are found to be better in generating lift. The effect of various bending wing configurations (F 1 , F 2 , F 3 and F 4) and different methods of imposing the bending (W 1 , W 2 and W 3) is studied. It was demonstrated that applying wing bending only during the downstroke phase (W 2) is more effective than imposing bending throughout the flapping cycle (W 1). Moreover, an effort is made to replicate the bending configuration observed in manta ray fish (W 3) to investigate its impact on flow domain characteristics, lift, and thrust forces. Furthermore, the inclusion of a winglet is found to significantly enhance lift generation. In addition to the study of bending effects on aerodynamic performance, the study also seeks to emulate a unique aspect of bat flight kinematics, specifically the dynamic variation in wing span length during flapping. In a comparative analysis of two span length variation strategies, it is discerned that exclusively varying span length during the upstroke phase is the optimal approach for achieving increased lift generation. The study highlights the crucial role of wing bending and span length modulation in achieving elevated lift forces while simultaneously reducing drag. These findings are seen as holding significant promise for the design and optimization of Micro Air Vehicles (MAVs) utilizing flapping-based lift generation mechanisms, contributing substantially to the identification of optimal parameters for enhancing MAVs' aerodynamic performance and operational efficiency. [ABSTRACT FROM AUTHOR]

Active suspension technique normally provides the best vibration mitigation performance at the cost of high-energy consumption. In contrast, the energy consumption of a semi-active suspension is normally much smaller than that of an active suspension, whereas the control performance is compromised as well. Observing the core issue that caused such a phenomenon is that the existing semi-active control force, unlike the active control force, shall always oppose to the relative motion of the actuator (i.e. clipping phenomenon). This paper subsequently proposes a novel semi-active vehicle suspension system that incorporates a passive negative stiffness (NS) spring and a semi-active damper (SD) to realize uncompromised active control force while consuming energy of a typical semi-active suspension system. In specific, the proposed system allows for decomposition of the target active control force and tracked via the collaboration of the NS and SD components. Herein, the NS element is capable of releasing the store potential energy that subsequently eases the aforementioned clipping phenomenon of a traditional semi-active suspension. In this paper, besides the relevant clarifications on the system topology and working mechanism, its feasibility and performance enhancement are also validated via systematic numerical simulations of a vehicle suspension; and the results indicate, for the first time, that the proposed semi-active suspension can fully track the active control force and subsequently achieve unprecedented control performance comparable to an active controller. [ABSTRACT FROM AUTHOR]

The micromixer is an important prerequisite for realizing the function of the microfluidic chip system. Micromixers are mainly used in protein crystallization, biological reactions, drug delivery and other fields. Efficient micromixers enable fast bioreaction processes. In this paper, according to the principle of plane geometry, micromixers with three different structural obstacles, circular, equilateral triangle and square, are designed to study how to improve the mixing efficiency of the micromixer. In this paper, the influence of the obstacle structure on the mixing efficiency and pressure drop of the micromixer is analyzed. Through numerical simulation, the results show that when Re = 100, the mixing efficiency of the circular obstacle micromixer is up to 97.4%, and the pressure drop is 15,789.597 Pa. In addition, this paper analyzes that the use of cylindrical obstacles can make the fluid generate horizontal and vertical vortex flow, break the usual laminar flow, and significantly improve the mixing efficiency. [ABSTRACT FROM AUTHOR]

In this paper, we introduce constant-yield prey harvesting into the Holling–Tanner model with generalist predator. We prove that the unique positive equilibrium is a cusp of codimension 4. As the parameter values change, the system exhibits degenerate Bogdanov–Takens bifurcation of codimension 4. Using the resultant elimination method, we show that the positive equilibrium is a weak focus of order 2, and the system undergoes degenerate Hopf bifurcation of codimension 2 and has two limit cycles. By numerical simulations, we demonstrate that the system exhibits homoclinic bifurcation and saddle–node bifurcation of limit cycles as the parameters are varied. The main results show that constant-yield prey harvesting and generalist predator can lead to complex dynamic behavior of the model. [ABSTRACT FROM AUTHOR]

This paper investigates a two-species amensalism model that includes the fear effect on the first species and the Beddington–DeAngelis functional response. The existence and stability of possible equilibria are investigated. Under different parameters, there exist two stable equilibria which means that this model is not always globally asymptotically stable. Together with the existence of all possible equilibria and their stability, saddle connection and close orbits, we derive some conditions for transcritical bifurcation and saddle-node bifurcation. Furthermore, global dynamics analysis of the model is performed. It is observed that under certain parameter conditions, when the intensity of the fear effect is below a certain threshold value, as the fear effect increases it will only reduce the density of the first species population and will have no influence the extinction or existence of the first species population. However, when the fear effect exceeds this threshold, the increase of the fear effect will accelerate the extinction of the first species population. Finally, numerical simulations are performed to validate theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the dynamical behaviors of a discrete-time fractional-order population model are considered. The stability analysis and the topological classification of the model at the fixed point have been investigated. It is shown that the model undergoes flip and Neimark–Sacker bifurcations around the co-existence fixed point by using the bifurcation and the normal form theory. These bifurcations lead to chaos when the parameter changes at critical point. In order to control chaotic behavior in the model result from Neimark–Sacker bifurcation, the OGY feedback method has been used. Furthermore, some numerical simulations, including bifurcation diagrams, phase portraits and maximum Lyapunov exponents of the presented model are plotted to support the correctness of the analytical results. The positive Lyapunov exponents demonstrate that chaotic behavior exists in the considered model. [ABSTRACT FROM AUTHOR]

In this paper, a reliable and effective local discontinuous Galerkin (LDG) scheme for numerically solving the classical Rosenau–Hyman equation with non-periodic boundary conditions has been proposed. This study employs the third-order nonlinearly stable total variation diminishing Runge–Kutta method and the LDG method, respectively, to discretize the temporal and spatial derivatives. Finally, numerical simulations are performed on various test problems and compared with the exact results as well as results produced by a few other numerical methods, to analyze the reliability and efficiency of the proposed method. The results generated, which validate the expected order of accuracy, are presented through multiple tables. In addition, several graphical representations of the problem are presented to depict the behavior of the solution. [ABSTRACT FROM AUTHOR]

In this paper, we consider a spatially size–stage-structured population dynamics model with resting phase. The primary objective of this model is to study size structure, stage structure, resting phase and spatial location simultaneously in a single population system. At first, we reformulate the problem as an abstract nondensely defined Cauchy problem. Then, taking advantage of the integrated semigroup and bifurcation theories, we investigate the stability and Hopf bifurcation at the positive equilibrium of the model. Finally, numerical simulations are presented as evidence to support our analytical results. A discussion of related problems is also presented briefly. [ABSTRACT FROM AUTHOR]

Many discrete systems have more distinctive dynamical behaviors compared to continuous ones, which has led lots of researchers to investigate them. The discrete predator–prey model with two different functional responses (Holling type I and II functional responses) is discussed in this paper, which depicts a complex population relationship. The local dynamical behaviors of the interior fixed point of this system are studied. The detailed analysis reveals this system undergoes flip bifurcation and Neimark–Sacker bifurcation. Especially, we prove the existence of Marotto's chaos by analytical method. In addition, the hybrid control method is applied to control the chaos of this system. Numerical simulations are presented to support our research and demonstrate new dynamical behaviors, such as period-10, 19, 29, 39, 48 orbits and chaos in the sense of Li–Yorke. [ABSTRACT FROM AUTHOR]

In this paper, we aim to minimize the epidemic size of tungiasis disease and economic costs simultaneously, with terminal demands for infected humans. A human–jigger parasite control system with four control schemes for humans and jiggers is established. We propose a multi-objective optimal control problem with terminal constraints, in which the accumulated number of infected humans and control costs are involved. By applying the modified normal boundary intersection algorithm and the interior point scheme, numerical simulations for different combinations of control schemes are carried out, and actual data in Madagascar are used. Effective combination schemes are indicated from the perspectives of disease eradication, cost saving and time saving. Once these effective combinations are properly performed, the disease can be controlled. When only minimizing the epidemic size, the combination of the optimal treatments and adulticiding efforts is the best choice in the rainy season; the combination of the optimal personal protections and treatments is the preferential option in the dry season. When only minimizing the economical cost, the combination of the optimal adulticide and larvicide is the better selection in the rainy season; the combination of the optimal personal protections, treatments and adulticiding efforts is the prior choose in the dry season. Thus, there is a trade-off between the two objectives for all the effective combinations, decision-makers may choose an appropriate one to control the disease. [ABSTRACT FROM AUTHOR]

This paper focuses on the dynamics of a submerged compound pendulum (SCP). The considered pendulum consists of a horizontal cylindrical element at its lowermost portion and a plate between the cylindrical element and the pivot. An approximate analytical expression for the natural frequency of the submerged compound pendulum is proposed. Further, a two-dimensional (2D) numerical model of the pendulum is developed using ANSYS (FLUENT). The natural periods of the SCP are determined for different geometric configurations. The analytically estimated natural periods of the pendulum match well with those obtained from numerical simulation. [ABSTRACT FROM AUTHOR]

The isolation technologies are adopted to protect the long-span space structures from serious damage under the action of earthquakes. When the isolation system is applied to the space structures, both horizontal and vertical vibration control effects on the structures should be concerned. In this paper, a two-dimensional earthquake isolation and mitigation device (TEIMD) composed of a high-damping viscoelastic (VE) core pad and VE dampers is proposed. Based on the dynamic shear experiment results of the VE damper, the energy dissipation capability of VE material is preferable. Then, the nonlinear equivalent stiffness and equivalent damping ratio of the TEIMD in horizontal and vertical directions are evaluated by using the numerical simulation method. The TEIMDs are arranged on the column top of a double-layer grid structure to assess the isolation effectiveness of the novel device. The dynamic analysis results of the double-layer grid structure with and without TEIMD reveal that this novel device can significantly reduce the acceleration response of the upper grid by relying on the strong energy dissipation performances in the horizontal and vertical directions. This research also verifies the feasibility of applying the TEIMD to the double-layer grid structure, which can effectively dissipate the vertical vibration energy of the structure. [ABSTRACT FROM AUTHOR]

This paper considers predator–prey systems in which the predator adapts the search speed to prey's density. The prey admits the cost of fear because of the predator and moves between source–sink patches to escape from predation. Using dynamical systems theory, we demonstrate equilibrium stability, uniform persistence and bifurcations in the system. It is shown that enhancing the search speed of predator and/or decreasing prey's dispersal from the source to sink could promote persistence of the system, while increasing the fear cost would stabilize the system. Moreover, dispersal could make the prey persist in both source–sink patches, even drive the predator into extinction. The dispersal could also make the prey reach a total population abundance larger than that without dispersal, even larger than the carrying capacity. Asymmetry in dispersal plays a role in the persistence and abundance. A novel finding of this work is that dispersal may lead to results reversing those without dispersal. Numerical simulations illustrate and extend our results. This work is important in understanding complexity in predation systems. [ABSTRACT FROM AUTHOR]

In this paper, rich dynamics and complex bifurcations of an SIR epidemic model with saturated incidence rate and strong Allee effect are investigated. First, the existence of disease-free and endemic equilibria is explored, and we prove that the system has at most three positive equilibria, which exhibit different types such as hyperbolic saddle and node, degenerate unstable saddle (node) of codimension 2, degenerate saddle-node of codimension 3 at disease-free equilibria, and cusp, focus, and elliptic types Bogdanov–Takens singularities of codimension 3 at endemic equilibria. Second, bifurcation analysis at these equilibria are investigated, and it is found that the system undergoes a series of bifurcations, including transcritical, saddle node, Hopf, degenerate Hopf, homoclinic, cusp type Bogdanov–Takens of codimensional 2, and focus and elliptic type Bogdanov–Takens bifurcation of codimension 3 which are composed of some bifurcations with lower codimension. The system shows very rich dynamics such as the coexistence of multiple periodic orbits and homoclinic loops. Finally, numerical simulations are conducted on the theoretical results. [ABSTRACT FROM AUTHOR]

This paper presents an innovative and efficient method for solving the fractional-order Van der Pol impulsive system. In particular, the proposed scheme utilizes finite difference techniques for approximating fractional integrals, and its efficacy is compared to existing integration methods presented in the literature. Moreover, the proposed approach is applied to fractional impulsive systems, specifically the Fractional Van der Pol system with impulse behavior. The results demonstrate the effectiveness of the impulsive treatment effects for the system under consideration. In general, this study offers an insightful contribution to the field of fractional calculus, while providing a practical and efficient solution for solving impulsive systems. [ABSTRACT FROM AUTHOR]

This paper analyzes an allelopathic phytoplankton competition model, which was proposed by Bandyopadhyay [Dynamical analysis of a allelopathic phytoplankton model, J Biol Syst14(02):205–217, 2006]. Our study refines the previous results and finds at most three positive equilibria for the system. The existence conditions of all positive equilibria and the corresponding stability cases are given in the paper. Interesting dynamical phenomena such as bistability, saddle-node bifurcation, and cusp bifurcation are found. It is shown that the rate of toxin releases heavily influences the positive equilibria of the system under certain conditions. Numerical simulations verify the feasibility of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we propose and investigate a delayed diffusive predator–prey model affected by toxic substances. We first study the boundedness and persistence property of the model. By analyzing the associated characteristic equation, we obtain the conditions for the existence of steady state bifurcation, Hopf bifurcation and Turing bifurcation. Furthermore, we also study the Hopf bifurcation induced by the delay. Finally, our theoretical results are verified by numerical simulation. The numerical observation results are in good agreement with the theoretically predicted results. Theoretical and numerical simulations indicate that toxic substances have a great impact on the dynamics of the system. [ABSTRACT FROM AUTHOR]

The spread of infectious diseases often presents the emergent properties, which leads to more difficulties in prevention and treatment. In this paper, the SIR model with both delay and network is investigated to show the emergent properties of the infectious diseases' spread. The stability of the SIR model with a delay and two delay is analyzed to illustrate the effect of delay on the periodic outbreak of the epidemic. Then the stability conditions of Hopf bifurcation are derived by using central manifold to obtain the direction of bifurcation, which is vital for the generation of emergent behavior. Also, numerical simulation shows that the connection probability can affect the types of the spatio-temporal patterns, further induces the emergent properties. Finally, the emergent properties of COVID-19 are explained by the above results. [ABSTRACT FROM AUTHOR]

Recurrence lacunarity has been recently proposed to detect dynamical state transitions over various temporal scales. In this paper, we combine suggested distribution moments and introduce multifractal recurrence lacunarity to unearth rich information of trajectories in phase space. By considering generalized moments, it provides an enhanced measurement to account for differences of black pixels in the recurrence plot at various scales. Numerical simulations have proved that the proposed method is able to differentiate varying types of time series and provide further insights of inherent features including stochastic series, chaotic maps and series contaminated interference components. In real-world applications, it performs well on quantifying the subtle structural changes of financial time series. In addition, it is intriguing to confirm that corrugation signals possess much more vivid information of heterogeneity in terms of recurrence plots than normal ones. [ABSTRACT FROM AUTHOR]

Based on the feature of piecewise linear (PWL) functions, a nonlinear feedback of a higher-order system can be transformed to an approximately equivalent PWL function so as to ease system implementation in engineering. As an example, a cubic feedback term can be approximately equivalently transformed to be a PWL function. Since the PWL function can be expressed by many simple functions such as signum function and absolute-valued function, the cubic term can be approximately equivalently replaced with these functions. Consequently, the method of approximate equivalence is employed in the JCS-08-13-2022 (JCS) chaotic system for simple circuit design and implementation. In this approach, the widely used multipliers are avoided and the circuits become more economical and also more robust. In this paper, the cubic Chua's resistor is equivalently approximately replaced by a PWL function. To show the effectiveness of the approximate equivalence, numerical simulations are demonstrated and verified by circuit implementation. [ABSTRACT FROM AUTHOR]

The study of rumor propagation dynamics is of great significance to reduce false news and ensure the authenticity of news information. In this paper, a SI reaction-diffusion rumor propagation model with nonlinear saturation incidence is studied. First, through stability analysis, we obtain the conditions for the existence and local stability of the positive equilibrium point. By selecting suitable variable as the control parameter, the critical value of Turing bifurcation and the existence theorem of Turing bifurcation are obtained. Then, using the above theorem and multi-scale standard analysis, the expression of amplitude equation around Turing bifurcation point is obtained. By analyzing the amplitude equation, different types of Turing pattern are divided such as uniform steady-state mode, hexagonal mode, stripe mode and mixed structure mode. Further, in the numerical simulation part, by observing different patterns corresponding to different values of control variable, the correctness of the theory is verified. Finally, the effects of different network structures on patterns are investigated. The results show that there are significant differences in the distribution of users on different network structures. [ABSTRACT FROM AUTHOR]

A liquid bath vibrating vertically can lead to the emergence of a self-propelled walking droplet on its free surface, which can exhibit chaotic motion. It is well-known that trajectories of a chaotic system are sensitive to its initial condition, known as the "butterfly-effect", while its statistics normally remain stable to small disturbances: this type of chaos is called "normal-chaos". However, a concept called "ultra-chaos" has been recently introduced, whose statistical features are unstable, i.e. extremely sensitive to small disturbances. Up to now, a few examples of ultra-chaos have been reported. In this paper, the influence of tiny disturbances on the motion of walking droplet is investigated. It is found that both normal-chaos and ultra-chaos exist in the motion of the walking droplet. Different from the normal-chaotic motion, even the statistical properties of the droplet's ultra-chaotic motion are sensitive to tiny disturbances. Therefore, this illustrates once again that ultra-chaos indeed exists widely and represents a higher disorder compared with normal-chaos. The ultra-chaos as a new concept can widen our knowledge about chaos and provide us with a new point of view to study chaotic properties. It should be emphasized that, for an ultra-chaos, it is impossible to repeat any results of its physical experiments or numerical simulations even in the meaning of statistics! Unfortunately, reproducibility is a corner stone of modern science. Thus, the paradigm of modern scientific research might be invalid for an ultra-chaotic system. [ABSTRACT FROM AUTHOR]

The operator-splitting (OS) method for real-time substructure testing (RTST) provides explicit and unconditionally stable solutions for structures with softening type stiffness and damping has been widely used for precisely disclosing the seismic performance of structures with velocity-dependent specimens. However, the OS method for RTST provides only explicit target displacement and velocity but not an explicit target acceleration, so that it is essentially an implicit method for Dynamic real-time substructure testing (DRTST) with dynamic system specimens. For precisely disclosing the seismic performance of multiple-degree-of-freedom structures with dynamic system specimens, one improved OS method is proposed for DRTST in this paper. The methodology and stability of the proposed OS method are investigated, and the effectiveness of the proposed OS method is validated by numerical simulations and experimental tests. By using the predictor displacement, velocity, and acceleration approximations, the OS method is an explicit algorithm for DRTST. The stability analysis shows that the proposed OS method is conditionally stable for DRTST, and its stability limit decreases with the increase of the mass ratio and the stiffness ratio, while it increases first and then decreases with the increase of the damping ratio. The numerical and experimental results confirm the stability and accuracy of the OS method. The OS method for DRTST provides a practical and precise investigation strategy for structures with dynamic system specimens and may have broad application prospects in civil engineering. [ABSTRACT FROM AUTHOR]

A new conservative chaotic system with a cubic root is constructed in this paper. The system has no equilibria. An offset parameter is introduced into the system. By modulating different offset parameters and corresponding initial conditions, multiple coexisting conservative chaotic attractors can be generated consequently. By replacing the offset parameter with an appropriate sign function, multiscroll conservative chaotic attractors can be generated effectively by connecting multiple coexisting chaotic attractors based on offset boosting. Moreover, the number of scrolls tend to be infinite. Finally, a novel chaotic circuit with a cubic root is designed successfully by connecting two multipliers in opposite directions. The hardware implementation of the chaotic circuit is also completed to further verify the existence of conservative chaos and the consistency with the numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the complex dynamics of a mapping derived from a differential equation with simple time-periodic delay. Firstly, we calculate the truncated normal form of 1:1 resonance of the mapping at a degenerate fixed point and obtain an approximating system of the mapping by using Picard iteration. By analyzing the approximate system, we find that the mapping will undergo a 1:1 resonance at the degenerate fixed point. Secondly, the qualitative property and the stability of the degenerate fixed point are determined, which provide a new view to understand the dynamic of differential equation with simple time-periodic delay. However, the approximate system does not have the versal unfolding of the Bogdanov–Takens singularity of codimension 2. These phenomena show that simple time-periodic delay can support complex dynamics. Finally, a numerical simulation is carried out to verify the analytic results. [ABSTRACT FROM AUTHOR]