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In predator–prey interactions, the effect of fear is an important factor in building ecological communities, affecting biodiversity, and maintaining ecological balance. In this paper, we present a specific predator–prey model that incorporates the effects of fear on prey populations by focusing on non-overlapping generations. Our study aims to explore the existence of biologically feasible equilibrium points and to analyze local asymptotic behavior around these points. Furthermore, using the center manifold theorem and the normal form theory of bifurcations, we study period-doubling bifurcations about prey-free and interior (positive) fixed points. On the other hand, the Neimark-Sacker bifurcation around the positive equilibrium point is investigated by applying the bifurcation theory of normal forms. We study the existence of chaos and present effective strategies to control the fluctuating and chaotic behaviors in the system using various chaos control techniques. Numerical simulations are presented to illustrate the theoretical discussion. [ABSTRACT FROM AUTHOR]

This study aims to explore the complexity of a discrete-time predator–prey system with a weak Allee effect. The existence and stability of fixed points, as well as period-doubling and Neimark–Sacker bifurcations, are all investigated. The system’s bifurcating and fluctuating behavior is controlled using feedback and hybrid control techniques. Additionally, numerical simulations are performed as evidence to support theoretical results. From an ecological perspective, these findings suggest that the Allee effect plays a pivotal role in shaping predator–prey dynamics. The moderate Allee effect fosters stability in both predator and prey populations, promoting coexistence and persistence within ecosystems. However, the disproportionate impact on predator populations underscores predators’ vulnerability to changes in prey behavior and availability, highlighting the importance of considering indirect effects in ecological modeling and conservation efforts. [ABSTRACT FROM AUTHOR]

In this paper, we explore the complex dynamical behavior of a discrete predator–prey system incorporating the prey immigration effect, which is transformed from a continuous model to a discrete system by utilizing nonstandard finite difference scheme. We analyze the stability conditions to better understand the behavior of the system when we include or exclude the immigration effect in the discrete system. Furthermore, we demonstrate that the discrete system undergoes supercritical Neimark–Sacker bifurcation when the bifurcation parameter passes through a critical value. We also study the state feedback chaos control strategy for the discrete system and we obtain the triangular region restricted by the lines that contain stable eigenvalues. Moreover, we illustrate phase portraits, maximum Lyapunov exponents, and bifurcation diagrams for the discrete system. We present the numerical simulations to validate the theoretical findings. Finally, with the advantage of the nonstandard finite difference discretization method, we eliminate the flip bifurcation that occurs when Euler discretization is used. [ABSTRACT FROM AUTHOR]

For achieving the goals of carbon peaking and carbon neutrality, the government will further strengthen subsidies to enterprises for carbon emission reduction. This paper investigates the long-term repeated game behavior of manufacturer and retailer in multichannel supply chains under three different forms of government subsidies. The long-term repeated game behavior of manufacturer and retailer is studied under the manufacturer green innovation subsidy model (IS model), manufacturer production subsidy model (MS model) and retailer sales subsidy model (RS model). Under three situations, excessive price adjustment can easily lead to system instability and sharp fluctuations in profits. Two methods are used for chaos control and management, and the parameter adjustment control method is found having more advantages for system re-stabilization. [ABSTRACT FROM AUTHOR]

In this paper, we present a mathematical model to lower the probability of breast cancer risk of the Breast Imaging Reporting and Data Systems (BI-RADS) 4 subcategories with the fractal fractional operator. This method improves evaluation quality, creates straightforward concepts for the early detection of breast cancer, and outcomes can be tracked easily by using BI-RADS-4 subcategories data at the Near East University Hospital. It uses the Banach fixed point theorem for nonlinear functional analysis and confirms the boundedness and uniqueness of solutions. Sensitivity analysis was performed on model parameters, and advanced numerical techniques were used to develop solutions. Also, this reveals disease-free and endemic equilibrium points, indicating local and global asymptotic stability. Chaos control was used in the regulated for linear responses approach to bring the system to stabilize according to its points of equilibrium. The growing procedure yields more effective and similar outcomes than the rotting technique, which happens quickly in the lowest fractional orders. Using Lagrange polynomial insight into the fractal-fractional operator, we conducted simulations and presented a comparative analysis in graphical form with classical and non-integer derivatives. The comparison of integer and non-integer results highlighted the importance of accurate fractional parameters in simulation. Moreover, it suggests that fractional operator-included mathematical models can help reveal more significant decisions on managing such real-life problems. Numerical simulations reveal absorption features for the fractal-fractional derivative with a generalized Mittag-Leffler kernel. The approximation solution approach allows for different order and dimension between 0 and 1, with outcomes changing for different fractional and fractal orders. It was determined that early diagnosis, quitting smoking, higher lactation rates, and ongoing care can reduce cancer risk. Our findings are critical for researchers, policymakers, and health care practitioners in combating and preventing breast cancer, contributing to worldwide public health initiatives.

This article presents an analysis and control approach for a non-smooth air-gap permanent magnet synchronous motor (NSAG-PMSM) in the absence of external disturbances. The analytical study of NSAG-PMSM shows the existence of equilibrium points. Based on the Routh–Hurwitz criterion, the stability of the equilibrium points reveals the existence of transcritical bifurcation. NSAG-PMSM exhibits various dynamical behaviours, such as bistable chaos, periodic spiking oscillations, chaotic spiking characteristics, coexistence between periodic and chaotic behaviours and periodic evolution towards monostable chaos as system parameters change. The research uses microcontroller implementation to validate the dynamical characteristics observed during the numerical simulations of the NSAG-PMSM. The study of NSAG-PMSM proposes a strategy to mitigate chaos and stabilise the system using two simple controllers, with a comparative study presented using peak overshoot and settling time diagrams. By combining these different aspects, this article significantly contributes to the understanding of the operation in NSAG-PMSM, highlighting specific aspects related to the application of microcontroller techniques in the field of electrical engineering and solutions to chaos control. [ABSTRACT FROM AUTHOR]

In this paper, the nonlinear phenomenon including hump and chaos analysis along with chaos control of an active suspension in vehicles has been studied. The unstable periodic orbits of the system are stabilized using the novel developed delay feedback control algorithm based on the fuzzy sliding mode system. The chaotic Equations of motions are derived via Newton-Euler relations then, the nonlinear phenomenon such as jump and chaos in the vehicle dynamics has been confirmed using forcing frequency method. The results of the forcing frequency demonstrate the changes in system behaviour from the periodic to the irregular chaotic responses. In order to eliminate the chaotic responses in the vertical dynamics of the vehicle, a new fuzzy sliding delay feedback control algorithm is designed on the active suspension. The controller gain of the sliding feedback control is online estimated via fuzzy logic causing to rejection of the chattering phenomenon in the sliding mode algorithm besides the improvement in the responses of the feedback system. Simulation results of the control system depict a reduction of settling time and energy consumption along with eliminating the overshoots and chaotic vibrations.

Permanent magnet synchronous motor (PMSM) is a multivariable and highly coupled nonlinear system, which is prone to chaotic behavior during actual operation. In order to suppress the chaotic behavior of the PMSM, this work designs a free-will arbitrary time adaptive controller based on the inverse step derivation, adaptive control theorem and Lyapunov stability theory. Firstly, the corresponding coordination transformations are designed according to the PMSM. Secondly, the bounded problem of the controlled system is analyzed by using the Lyapunov stability theory, and the free-will arbitrary time adaptive controller is designed by backstepping derivation. Finally, numerical simulation verifies that the designed controller quickly stabilizes the system state variables to the output signals and proves that the controller is free-will arbitrary time stable for all closed-loop signals. [ABSTRACT FROM AUTHOR]

Aiming at the rich bifurcation and chaotic characteristics in the inverter with proportion integral derivative (PID) controller, the discrete iterative model of such an inverter was derived based on the stroboscopic mapping theory; the nonlinear evolution and the cause of instability in this inverter are analyzed. It was observed that the low‐frequency oscillation following instability was due to the Hopf bifurcation, which will decrease the power supplied quality by the inverter. To address the potential issue of the system instability caused by nonlinear behaviors, an improved exponential time‐delay feedback control scheme was proposed. The controlled object's output current first subtracted its own delay a period of time to form a difference term, which was subsequently fed into an exponential link to make difference with the constant 1. The resulting value was then fed into a proportional link to obtain the control term, which was applied to the PID controlled inverter in a feedback manner. Moreover, the range of the feedback proportional coefficient was solved via the Jury criterion. Finally, the effectiveness of this scheme was verified through the comparative simulations, demonstrating that this scheme can not only increase the stability domain for each parameter by more than 50% in the PID controlled inverter but also stabilize the quasi‐periodic behavior due to the low scale oscillation caused by the Hopf bifurcation at the switching frequency. [ABSTRACT FROM AUTHOR]

We describe the period-bubbling attractors, their generation mechanism and chaos control strategy in nonlinear, unidimensional and two-parameter-dependent discrete maps. A theorem for the occurrence of sequential period-bubbling attractors leading to chaos, is presented. It delineates the role of a geometric parameter in the formation of anti-monotonic periodic sequences of each iterate of such discrete maps. The appearances of different period bubbles in two distinct Gaussian and cubic maps are demonstrated in accordance to the theorem. The delimited chaos through period-bubbling route is suppressed by employing linear density feedback with a proportional constant. The study discloses that the period-bubbling transitional route in unidimensional map cannot be suppressed by adopting constant feedback, which is in contrast to the control of period-doubling route to chaos. In Gaussian and cubic maps, the period-bubbling routes to chaos are gradually collapsed for linear density feedbacks, with the enhancements of the feedback strength parameter k. Interestingly, at k = 1 , the feedback-influenced Gaussian map experiences tangent bifurcation and chaos can re-enter into its dynamics through that scenario for k > 1. The tangent bifurcation in the feedback-affected Gaussian map is explained mathematically. However, no such transitional exchange has been perceived in cubic map, for augmented values of the feedback strength parameter. [ABSTRACT FROM AUTHOR]

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

Finite-time control theory has been widely used as a mathematical tool to design robust controllers. By manipulating the finite-time convergence proof of this theory, we developed a new control design appropriately tuned for the finite-time control of the chaotic logistics system. In this experimental setup, the logistic equation is programmed into a PIC microcontroller, and a part of the controller was conceived using analog electronics. Because the system to be controlled is in the discrete-time domain, and the finite-time stability proof is stated in the continuous-time representation, our finite-time control approach is a good example for designing control algorithms in both time domain schemes. Hence, our experimental results support our main contribution. Pulse width modulation (PWM) is the format used to translate digital signals into the continuous-time field. Therefore, the main contribution of this article is the theoretical foundations for creating a recent controller that satisfies the convergence criterion in finite time and its construction using an 8-bit microcontroller. All this contributes to the chaotic logistical map. [ABSTRACT FROM AUTHOR]

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

Understanding and accounting for the slow–fast effect are crucial for accurately modeling and predicting the dynamics of predator–prey models, emphasizing the importance of considering the relative speeds of interacting populations in ecological research. This paper examines a predator–prey interaction to study its complex dynamics due to its slow–fast effect on predator populations. The occurrence and stability of equilibria are analyzed. The stability of positive fixed point is dependent on the slow–fast effect parameter ϵ$$ \epsilon $$, which must fall within a specific range when the generation gap is larger. The positive fixed point becomes unstable for bigger values of ϵ$$ \epsilon $$ because the growth of predators is faster, resulting in the extinction of all prey. Smaller values of ϵ$$ \epsilon $$ cause the positive fixed point to become unstable since the prey grows more quickly while the predator grows more slowly, ultimately causing the extinction of the predator. Moreover, it is shown that Leslie–Gower model experiences Neimark–Sacker and period‐doubling bifurcations at positive equilibrium point. In order to control bifurcation, hybrid control and feedback control methods are employed. Finally, analytical results are confirmed by numerical examples. [ABSTRACT FROM AUTHOR]

The single-phase photovoltaic energy storage inverter represents a pivotal component within photovoltaic energy storage systems. Its operational dynamics are often intricate due to its inherent characteristics and the prevalent usage of nonlinear switching elements, leading to nonlinear characteristic bifurcation such as bifurcation and chaos. In this paper, a deep investigation of a single-phase H-bridge photovoltaic energy storage inverter under proportional–integral (PI) control is made, and a sinusoidal delayed feedback control (SDFC) strategy to mitigate the nonlinear characteristics is proposed. A frequency domain mapping model of the system is established, then, by analyzing the Jacobian matrix and equilibrium points, the bifurcation diagram is formed, and finally, the stable operational domains are determined under double and triple bifurcation parameters. Through simulation experiments, the efficacy of this strategy is validated. The findings show that through the control strategy, the stable operational envelope of the inverter can be greatly expanded and the nonlinear dynamic phenomena can be notably suppressed. [ABSTRACT FROM AUTHOR]

Current treatments of cardiac arrhythmias like ventricular fibrillation involve the application of a high-energy electric shock, that induces significant electrical currents in the myocardium and therefore involves severe side effects like possible tissue damage and post-traumatic stress. Using numerical simulations on four different models of 2D excitable media, this study demonstrates that low energy pulses applied shortly after local minima in the mean value of the transmembrane potential provide high success rates. We evaluate the performance of this approach for ten initial conditions of each model, ten spatially different stimuli, and different shock amplitudes. The investigated models of 2D excitable media cover a broad range of dominant frequencies and number of phase singularities, which demonstrates, that our findings are not limited to a specific kind of model or parameterization of it. Thus, we propose a method that incorporates the dynamics of the underlying system, even during pacing, and solely relies on a scalar observable, which is easily measurable in numerical simulations. [ABSTRACT FROM AUTHOR]

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

This study discusses the dynamic behaviors of the prey–predator model subject to the Allee effect and the harvesting of prey species. The existence of fixed points and the topological categorization of the co-existing fixed point of the model are determined. It is shown that the discrete-time prey–predator model can undergo Flip and Neimark–Sacker bifurcations under some parametric assumptions using bifurcation theory and the center manifold theorem. A chaos control technique called the feedback-control method is utilized to eliminate chaos. Numerical examples are given to support the theoretical findings and investigate chaos strategies' effectiveness and feasibility. Additionally, bifurcation diagrams, phase portraits, maximum Lyapunov exponents, and a graph showing chaos control are demonstrated. [ABSTRACT FROM AUTHOR]

This work develops a quantum control application of many-body quantum chaos for ultracold bosonic gases trapped in optical lattices. It is long known how to harness exponential sensitivity to changes in initial conditions for control purposes in classically chaotic systems. In the technique known as targeting, instead of a hindrance to control, the instability becomes a resource. Recently, this classical targeting has been generalized to quantum systems either by periodically countering the inevitable quantum state spreading or by introducing a control Hamiltonian, where both enable localized states to be guided along special chaotic trajectories toward any of a broad variety of desired target states. Only strictly unitary dynamics are involved; i.e. it gives a coherent quantum targeting. In this paper, the introduction of a control Hamiltonian is applied to Bose–Hubbard systems in chaotic dynamical regimes. Properly selected unstable mean field solutions can be followed particularly rapidly to states possessing precise phase relationships and occupancies. In essence, the method generates a quantum simulation technique that can access rather special states. The protocol reduces to a time-dependent control of the chemical potentials, opening up the possibility for application in optical lattice experiments. Explicit applications to custom state preparation and stabilization of quantum many-body scars are presented in one- and two-dimensional lattices (three-dimensional applications are similarly possible). [ABSTRACT FROM AUTHOR]

The self-cascade (SC) method is an effective technique for chaos enhancement and complexity increasing in chaos maps. Additionally, the controllable self-cascade (CSC) method allows for more accurate control of Lyapunov exponents of the discrete map. In this work, the SC and CSC systems of the original map are derived, which enhance the chaotic performance while preserving the fundamental dynamical characteristics of the original map. Higher Lyapunov exponent of chaotic sequences corresponding to higher frequency are obtained in SC and CSC systems. Meanwhile, the Lyapunov exponent could be linearly controlled with greater flexibility in the CSC system. The verification of the numerical simulation and theoretical analysis is carried out based on the platform of CH32. [ABSTRACT FROM AUTHOR]

This paper examines dynamic behaviours of a two-species discrete fractional order predator-prey system with functional response form of Ivlev along with Gompertz growth of prey population. A discretization scheme is first applied to get Caputo fractional differential system for the prey-predator model. This study identifies certain conditions for the local asymptotic stability at the fixed points of the proposed prey-predator model. The existence and direction of the period-doubling bifurcation, Neimark-Sacker bifurcation, and Control Chaos are examined for the discrete-time domain. As the bifurcation parameter increases, the system displays chaotic behaviour. For various model parameters, bifurcation diagrams, phase portraits, and time graphs are obtained. Theoretical predictions and long-term chaotic behaviour are supported by numerical simulations across a wide variety of parameters. This article aims to offer an OGY and state feedback strategy that can stabilize chaotic orbits at a precarious equilibrium point. [ABSTRACT FROM AUTHOR]

Cascaded H-bridge inverters, which belong to strongly nonlinear time-varying system with complex dynamics, have been widely used in high-voltage and high-power engineering fields. In this paper, a carrier phase-shifted sinusoidal pulse-width modulation cascaded H-bridge inverter is taken as an example with piecewise analysis to establish the discrete iterative mathematical model. Furthermore, the nonlinear dynamic behavior of this inverter system is investigated using folding diagrams, spectrum diagrams, bifurcation diagrams, Lyapunov exponents, etc. We find that this inverter can exhibit multiperiod bifurcation, tangential bifurcation and paroxysmal chaos within certain ranges of control coefficients and other circuit parameters, which will influence the system's stability seriously. On the basis of this discovery, the sinusoidal time-delay feedback control method is proposed. The difference between the load current of the controlled object and its own delay is used to form a feedback term, which is then fed into the sine function and proportional link to obtain the control term. Moreover, the Jacobian matrix of this feedback inverter system is derived, and the constraints on the feedback control coefficient are obtained based on the Jury criterion. Simulation results have verified the effectiveness of such a sinusoidal time-delay feedback control method, which can improve the stability and anti-interference of the system. The research can be used to provide some reference and guidance for the circuit design, debugging and control of cascaded H-bridge inverters. [ABSTRACT FROM AUTHOR]

In this paper, the nonlinear phenomenon including hump and chaos analysis along with chaos control of an active suspension in vehicles has been studied. The unstable periodic orbits of the system are stabilized using the novel developed delay feedback control algorithm based on the fuzzy sliding mode system. The chaotic Equations of motions are derived via Newton-Euler relations then, the nonlinear phenomenon such as jump and chaos in the vehicle dynamics has been confirmed using forcing frequency method. The results of the forcing frequency demonstrate the changes in system behaviour from the periodic to the irregular chaotic responses. In order to eliminate the chaotic responses in the vertical dynamics of the vehicle, a new fuzzy sliding delay feedback control algorithm is designed on the active suspension. The controller gain of the sliding feedback control is online estimated via fuzzy logic causing to rejection of the chattering phenomenon in the sliding mode algorithm besides the improvement in the responses of the feedback system. Simulation results of the control system depict a reduction of settling time and energy consumption along with eliminating the overshoots and chaotic vibrations. [ABSTRACT FROM AUTHOR]

In this paper, a high dimensional double rotor model is proposed. We establish its dynamic equations, and simply it into a four-dimensional mapping form. The bifurcations of the double rotor mapping under different control parameters are investigated. The chaotic dynamic behavior of the model is controlled by improving the pole assignment method. With the linear control theory, a control parameter is selected and the period-1 is chosen as control target. When the mapping point wanders to the neighborhood of the periodic point, the control parameter is perturbed. The unstable period-1 orbit is controlled to be a stable periodic orbit. Numerical simulations are consistent with the theoretical analysis. The results of this research show that this chaos control method can be applied to the 4-dimensional model and can be realized.The research results indicate when the selected regulator poles are different, the control times are different. [ABSTRACT FROM AUTHOR]

This paper investigates the complex dynamical behavior of a discrete prey-predator system with a fear factor, a strong Allee effect, and prey refuge. The existence and stability of fixed points in the system are discussed. By applying the central manifold theorem and bifurcation theory, we have established the occurrence of various types of bifurcations, including flip bifurcation and Neimark-Sacker bifurcation. Furthermore, to address the observed chaotic behavior in the system, three controllers were designed by employing state feedback control, OGY feedback control, and hybrid control methods. These controllers serve to control chaos in the proposed system and identify specific conditions under which chaos or bifurcations can be stabilized. Finally, the theoretical analyses have been validated through numerical simulations.

Gear shifting mechanism is one of the most critical components in the shifting transmission system, and its performance directly affects the power performance and stability of the transmission system. In this study, the dynamic equations of the gear shifting mechanism of the two-stage planetary gear transmission system are established, and the influence of the external excitation frequency on the complex dynamic characteristics of the transmission system is studied. Through bifurcation diagram, time domain response diagram, phase diagram, Poincare section diagram and spectrum diagram, the chaotic vibration characteristics of the two-stage planetary gear transmission system are learned, and the stable vibration range of the external excitation frequency is obtained. The proportional differential control method is used to control the chaotic vibration of the gear shifting mechanism, and the chaotic vibration is adjusted to a stable single period vibration. The research results lay a foundation for improving the stability of the shift planetary transmission system.

This research paper focuses on investigating the dynamics and chaos control of two discrete systems corresponding to the singularly perturbed equation associated to the Hénon difference equation with continuous arguments. We investigate the local stability of the two systems. To achieve chaos control, we employ the state feedback control method for both systems. Numerical simulations are conducted to gain insights into the qualitative behavior of these systems. By conducting numerical simulations, we gain valuable insights into the role played by the perturbation parameter and the discrete delays in the bifurcation behavior of each system. Furthermore, we demonstrate the practical application of the chaos control method through the implementation of an on-off strategy.

In order to solve the dynamic analysis and chaotic motion control problems of the current-mode-controlled Boost converter system, a state equation model in the continuous current mode is established. The evolutionary path of the periodic motion of the system through the doubling bifurcation to the chaotic motion is analyzed by the bifurcation diagram, Poincaré sections and phase portraits. Then, according to the fundamental principle of the resonant parametric perturbation (RPP) method, a controller is designed based on the model-free adaptive control (MFAC) method to output the perturbation amplitude, and the disturbance quantity is calculated according to the perturbation amplitude. By adding a small amplitude disturbance to the controllable parameter of the controlled system, the chaotic motion of the system is guided to expected periodic orbit. The advantage of this method is that no precise mathematical model (PMM) of the system is required. At the same time, the design of the controller is simple and easy to implement. [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]

This study investigates the dynamics of predator–prey interactions with non-overlapping generations under the influence of fear effects, a crucial factor in ecological research. We propose a novel discrete-time model that addresses limitations of previous models by explicitly incorporating fear. Our primary question is: How does fear influence the stability of predator–prey populations and the potential for chaotic dynamics? We analyze the model to identify biologically relevant equilibria (fixed points) and determine the conditions for their stability. Bifurcation analysis reveals how changes in fear levels and predation rates can lead to population crashes (transcritical bifurcation) and complex population fluctuations (period-doubling and Neimark–Sacker bifurcations). Furthermore, we explore the potential for controlling chaotic behavior using established methods. Finally, two-parameter analysis employing Lyapunov exponents, spectrum, and Kaplan–Yorke dimension quantifies the chaotic dynamics of the proposed system across a range of fear and predation levels. Numerical simulations support the theoretical findings. This study offers valuable insights into the impact of fear on predator–prey dynamics and paves the way for further exploration of chaos control in ecological models. [ABSTRACT FROM AUTHOR]

The occurrence of cannibalism is common in natural colonies and can substantially affect the functional relationships between predators and prey. Despite the belief that cannibalism stabilizes or destabilizes predator–prey models, its effects on prey populations are not well-understood. In this study, we propose a discrete-time prey–predator model to examine the presence and local stability of biologically possible equilibria. We employ the center manifold theorem and normal theory to investigate the various types of bifurcations that arise in the system. The findings of our study reveal that the model exhibits transcritical bifurcation at its trivial equilibrium. In addition, the discrete-time predator–prey system demonstrates period-doubling bifurcation in the vicinity of both its boundary equilibrium and interior equilibrium. Furthermore, we analyze the existence of Neimark–Sacker bifurcation around the interior equilibrium point. We demonstrate that cannibalism in the prey population can lead to periodic outbreaks, but these outbreaks are limited to the prey population and do not affect predation. In order to regulate the periodic oscillations and other bifurcating and fluctuating behaviors of the system, various chaos control strategies are executed. Additionally, extensive numerical simulations are carried out to validate and substantiate the analytical findings. We utilized the software Mathematica 12.3, which is an efficient and effective computing tool that enables symbolic and numerical computations to carry out numerical simulations. [ABSTRACT FROM AUTHOR]

This article investigates the influence of chaos control and time delay on a chaotic surface energy balance-mass balance model of the Cryosphere. This research delves into the effectiveness of employing the active control method to stabilize chaotic systems with different fractional orders. Moreover, the investigation uncovers a noteworthy aspect of system dynamics, highlighting the role of time delay as a stabilizing element in chaotic systems. The generalized predictor-corrector method has been used to solve the fractional delayed and non-delayed systems. Numerical simulations show that the addition of time lag confers stability to the chaotic model for fractional orders a=land 0.95. Remarkably, for α = 0.90, 0.85, 0.80 and 0.75, the delayed model transitions into an asymptotically stable state, revealing the significant stabilizing effect of time delay. [ABSTRACT FROM AUTHOR]

This research paper focuses on investigating the dynamics and chaos control of two discrete systems corresponding to the singularly perturbed equation associated to the Hénon difference equation with continuous arguments. We investigate the local stability of the two systems. To achieve chaos control, we employ the state feedback control method for both systems. Numerical simulations are conducted to gain insights into the qualitative behavior of these systems. By conducting numerical simulations, we gain valuable insights into the role played by the perturbation parameter and the discrete delays in the bifurcation behavior of each system. Furthermore, we demonstrate the practical application of the chaos control method through the implementation of an on-off strategy. [ABSTRACT FROM AUTHOR]

In this study, our focus is on stabilizing a competitive game involving an original equipment manufacturer (OEM) and a third-party remanufacturer (TPR). To assess the presence of chaos within the dynamics of this game, we employ various analytical tools, including spectral entropy (SE), bifurcation diagrams, and Lyapunov exponents. The unpredictable nature of chaotic dynamics significantly influences the market and has negative implications for the strategic decisions of both firms. Our approach to counteracting this chaotic behaviour and stabilizing the system revolves around the implementation of the Ott, Grebogi, and Yorke (OGY) method. Crucially, our analysis highlights that the marginal costs ( c n and c r ) incurred by the OEM and TPR emerge as pivotal factors in achieving stabilization within the game. To provide a tangible demonstration of the effectiveness of our proposed stabilization strategy in the context of this competitive environment, we conducted numerical simulations. [ABSTRACT FROM AUTHOR]

Current treatments of cardiac arrhythmias like ventricular fibrillation involve the application of a high-energy electric shock, that induces significant electrical currents in the myocardium and therefore involves severe side effects like possible tissue damage and post-traumatic stress. Using numerical simulations on four different models of 2D excitable media, this study demonstrates that low energy pulses applied shortly after local minima in the mean value of the transmembrane potential provide high success rates. We evaluate the performance of this approach for ten initial conditions of each model, ten spatially different stimuli, and different shock amplitudes. The investigated models of 2D excitable media cover a broad range of dominant frequencies and number of phase singularities, which demonstrates, that our findings are not limited to a specific kind of model or parameterization of it. Thus, we propose a method that incorporates the dynamics of the underlying system, even during pacing, and solely relies on a scalar observable, which is easily measurable in numerical simulations.

In this paper, we present a dynamic model of syphilis. The goal of this work is to provide a mathematical model for syphilis disease that contains information about the suspect, infected, recovered, and exposed. Boundedness, positivity, and unique solutions at equilibrium points are used in the qualitative and quantitative study of a proposed model using the power law kernel. The Routh-Hurwitz stability criteria are used to address the model's local and global stability. Chaos control will use the regulate for linear responses approach to bring the system to stabilize according to its points of equilibrium. Using Lyapunov function tests, the global stability of free and endemic equilibrium points is confirmed. The Lipschitz condition and fixed point theory are utilized to satisfy the requirements for the existence and uniqueness of the exact solution. The generalized form of the power law kernel is solved using a two-step Lagrange polynomial method to investigate the impact of the fractional operator using numerical simulations that illustrate the effects of various parameters on the illness.

The refuge effect is critical in ecosystems for stabilizing predator-prey interactions. The purpose of this research was to investigate the complexities of a discrete-time predator-prey system with a refuge effect. The analysis investigated the presence and stability of fixed points, as well as period-doubling and Neimark-Sacker (NS) bifurcations. The bifurcating and fluctuating behavior of the system was controlled via feedback and hybrid control methods. In addition, numerical simulations were performed as evidence to back up our theoretical findings. According to our findings, maintaining an optimal level of refuge availability was critical for predator and prey population cohabitation and stability.

In this study, our focus is on stabilizing a competitive game involving an original equipment manufacturer (OEM) and a third-party remanufacturer (TPR). To assess the presence of chaos within the dynamics of this game, we employ various analytical tools, including spectral entropy (SE), bifurcation diagrams, and Lyapunov exponents. The unpredictable nature of chaotic dynamics significantly influences the market and has negative implications for the strategic decisions of both firms. Our approach to counteracting this chaotic behaviour and stabilizing the system revolves around the implementation of the Ott, Grebogi, and Yorke (OGY) method. Crucially, our analysis highlights that the marginal costs ($ c_n $ and $ c_r $) incurred by the OEM and TPR emerge as pivotal factors in achieving stabilization within the game. To provide a tangible demonstration of the effectiveness of our proposed stabilization strategy in the context of this competitive environment, we conducted numerical simulations.

The objective of this study was to analyze the complex dynamics of a discrete-time predator-prey system by using the piecewise constant argument technique. The existence and stability of fixed points were examined. It was shown that the system experienced period-doubling (PD) and Neimark-Sacker (NS) bifurcations at the positive fixed point by using the center manifold and bifurcation theory. The management of the system's bifurcating and fluctuating behavior may be controlled via the use of feedback and hybrid control approaches. Both methods were effective in controlling bifurcation and chaos. Furthermore, we used numerical simulations to empirically validate our theoretical findings. The chaotic behaviors of the system were recognized through bifurcation diagrams and maximum Lyapunov exponent graphs. The stability of the positive fixed point within the optimal prey growth rate range $ A_1 < a < A_2 $ was highlighted by our observations. When the value of $ a $ falls below a certain threshold $ A_1 $, it becomes challenging to effectively sustain prey populations in the face of predation, thereby affecting the survival of predators. When the growth rate surpasses a specific threshold denoted as $ A_2 $, it initiates a phase of rapid expansion. Predators initially benefit from this phase because it supplies them with sufficient food. Subsequently, resource depletion could occur, potentially resulting in long-term consequences for populations of both the predator and prey. Therefore, a moderate amount of prey's growth rate was beneficial for both predator and prey populations.

Amensalism, a rare yet impactful symbiotic relationship in ecological systems, is the focus of this study. We examine a discrete-time amensalism system by incorporating the fear effect on the first species. We identify the plausible equilibrium points and analyze their local stability conditions. The global attractivity of the positive equilibrium, $ E^* $, and the boundary equilibrium, $ E_1 $, are analyzed by exploring threshold conditions linked to the level of fear. Additionally, we analyze transcritical bifurcations and flip bifurcations exhibited by the boundary equilibrium points analytically. Considering some biologically feasible parameter values, we conduct extensive numerical simulations. From numerical simulations, it is observed that the level of fear has a stabilizing effect on the system dynamics when it increases. It eventually accelerates the extinction process for the first species as the level of fear continues to increase. These findings highlight the complex interplay between external factors and intrinsic system dynamics, enriching potential mechanisms for driving species changes and extinction events.

Chaos intermittency is composed of a laminar regime, which exhibits almost periodic motion, and a burst regime, which exhibits chaotic motion; it is known that in chaos intermittency, switching between these regimes occurs irregularly. In the laminar regime of chaos intermittency, the periodic solution before the saddle node bifurcation is closely related to its generation, and its behavior becomes periodic in a short time; the laminar is not, however, a periodic solution, and there are no unstable periodic solutions nearby. Most chaos control methods cannot be applied to the problem of stabilizing a laminar response to a periodic solution since they refer to information about unstable periodic orbits. In this paper, we demonstrate a control method that can be applied to the control target with laminar phase of a dynamical system exhibiting chaos intermittency. This method records the time series of a periodic solution prior to the saddle node bifurcation as a pseudo-periodic orbit and feeds it back to the control target. We report that when this control method is applied to a circuit model, laminar motion can be stabilized to a periodic solution via control inputs of very small magnitude, for which robust control can be obtained. [ABSTRACT FROM AUTHOR]

By using model discretization of the piecewise constant argument method, a discrete amensalism model with nonselective harvesting and Allee effect is formulated. The dynamic analysis of the model is studied and the existence and stability of the equilibrium point are discussed. The fold bifurcation and flip bifurcation at the equilibrium point of the system are proved by using the bifurcation theory and the center manifold theorem. In order to control flip bifurcation and restore the system to a stable state, a hybrid control strategy of parameter perturbation and state feedback is adopted. Finally, the effectiveness of the theoretical results and the control strategy is verified by numerical simulations. [ABSTRACT FROM AUTHOR]