Chaos Control Research Articles

Initial-offset and amplitude control of multi-scroll attractor in a chaotic jerk system

Abstract With the gradual deepening of research on chaos, in order to flexibly apply chaos, offset boosting and amplitude control have become a hot topic. However, few people have studied chaotic systems with multi-scroll attractor under initial conditions.
This paper constructs and analyzes a simple four-dimensional chaotic system. Unlike other extension methods that modify the original seed system, this method does not make any changes to the original seed system, only adds a new variable in the extension dimension. It is found that the proposed system can achieve offset boosting and amplitude control by changing the initial values, and the system has characteristics such as multi-scroll attractors, infinite equilibrium points, symmetry, and so on. Finally, FPGA hardware implementation was carried out to verify the numerical results.

A Comparative Analysis of Fractal and Fractionalized Thermal Non-Equilibrium Model for Chaotic Convection Saturated by Porous Medium

The convective heat transfer is one of the most important mechanism of heat transference for controlling the chaotic characteristics in porous media. A comparative study of thermal non-equilibrium model is proposed for fractal porous under the consideration of chaotic convection. A novel chaos control is focused between fractal porous and fractional porous by means of newly proposed differential and integral techniques. The sensitivity analysis for chaos expansion and uncertainty quantification for the flow in heterogeneous media have been perceived to the problem of chaotic convection through numerical simulations. In order to approximate the propagation of chaos, two types of simulations have been carried out in terms of chaotic attractors through fractal and fractional approaches. For examining a variety of chaos under the numerical simulations in which fractal domain is varied and fractional domain is fixed, fractal domain is fixed and fractional domain is varied, and both fractal as well as fractional domain are varied. Finally, it is observed that the fractional and fractal memory effects have caused by interactions between uncertain parameters and disclosed the microstructures on the permeability of porous media.

Chlamydia infection with vaccination asymptotic for qualitative and chaotic analysis using the generalized fractal fractional operator

In this work, we solve a system of fractional differential equations utilizing a Mittag-Leffler type kernel through a fractal fractional operator with two fractal and fractional orders. A six-chamber model with a single source of chlamydia is studied using the concept of fractal fractional derivatives with nonsingular and nonlocal fading memory. The fractal fractional model of the Chlamydia system can be solved by using the characteristics of a non-decreasing and compact mapping. A suggested model with the Lipschitz criteria and linear growth is studied both qualitatively and quantitatively, taking into account boundedness, uniqueness, and positive solutions at equilibrium points with Leray-Schauder results under time scale concepts. We examined the framework of local and global stability and insight into Lyapunov function properties for the infectious disease model. Chaos Control will employ the regulate for linear responses approach to stabilize the system following its equilibrium points. This will take into consideration a fractional order framework with a managed design, where solutions are bounded in the feasible domain and have a greater impact at the lower minimum infectious rate. To illustrate the implications of fractional and fractal dimensions with varying interest rate values through simulations with Newton’s polynomial method under the Mittag-Lefller kernel. Additionally, a comparative analysis of results is also derived by employing power and exponential decay kernels at various fractional orders.

Chaos and feasibility analysis of a healthy lifestyle’s sustainability using fractional-order polycystic ovarian syndrome’s effect on infertility

In this study, we developed a fractional-order model for polycystic ovarian syndrome issue transmission in women through four compartments with the Mittag-Leffler kernel. For biological feasibility, we discussed the positivity and boundedness of solutions with fixed point mappings in Banach spaces. Sensitivity analysis is performed using different variables as response functions each time, employing Latin Hyper-cube Sampling (LHS) and Partial Rank Correlation Coefficient (PRCC) with 200 iterations. Further, the reproductive number is determined for the model’s biological feasibility with an analysis of parameter impact through Matlab software. The solutions are examined for global stability using the Lyapunov function with a first derivative. Chaos Control will use the regulate for linear responses approach to bring the system to stabilize according to its points of equilibrium. Numerical solutions are derived by using a Newton polynomial in the generalized form of the Mittag-Leffler kernel, which illustrates the effect of the fractional operator and parameters involved in the system. Results are also analyzed with different assumptions of parameter values and initial conditions to observe the different impacts of treatment to overcome the risk of infertility in women. Such type of investigation will be useful to investigate the spread of disease as well as helpful in developing control strategies to overcome the risk of problems and best management care pre-detection of the issue and for treatment.

Modeling and analysis using piecewise hybrid fractional operator in time scale measure for ebola virus epidemics under Mittag–Leffler kernel

This emerging infectious disease poses one of the most severe threats to public health in these locations, but there are not many reliable therapies yet. In this work, we developed the Ebola virus dynamics and control factors epidemic model with a piecewise hybrid fractional Operator in time scale measure insight of Mittag–Leffler kernel. Patterns and structures that repeat at various scales are the focus of fractal analysis, which has applications in complex systems such as biological ones. Both qualitatively and statistically, a proposed model with the Lipschitz criteria and linear growth is examined, considering positive solutions, boundedness, and uniqueness at equilibrium points with Leray-Schauder results under time scale ideas. The regulation for linear responses approach will be used by Chaos Control to stabilize the system after its equilibrium points. A fractional-order framework with a controlled design will be considered, where solutions are bounded in the feasible domain of relations of different compartments. Ulam–Hyers stability results in the solution are treated when function (constant or rising) for the component of qualitative inquiry in generalized form. The dynamical behaviors of the suggested model are discussed with the Newton polynomial approach used to implement on model in the sense of classical piecewise and Mittag–Leffler kernel at different fractional order values. The model shows that solutions are stable and confined within a feasible range, ensuring reliability. Through detailed simulations, it effectively captures how different interventions and infection rates influence Ebola spread. This fractional-order model enhances understanding of Ebola transmission, providing a strong basis for predicting outbreaks and planning effective control measures, with practical applications for analyzing real-world data.

A three-dimensional discrete fractional-order HIV-1 model related to cancer cells, dynamical analysis and chaos control

In this paper, we study a three-dimensional discrete-time model to describe the behavior of cancer cells in the presence of healthy cells and HIV-infected cells. Based on the Caputo-like difference operator, we construct the fractional-order biological system. This study's significance lies in developing a new approach to presenting a biological dynamical system. Since the qualitative analysis related to existence, uniqueness, and stability is almost the same as can be found in numerous existing papers, and comparing this study to other research, constructing a biological discrete system using the Caputo difference operator can be particularly important. Using powerful tools of nonlinear theory such as phase plots, bifurcation diagrams, Lyapunov exponent spectrum, and the 0-1 test, we establish that the proposed system can exhibit different biological states, including stable, periodic, and chaotic behaviors. Here, the route leading to chaos is period-doubling bifurcation. Furthermore, the level of chaos in the system is quantified using $C_{0}$ complexity and approximate entropy algorithms. The stabilization or suppression of chaotic motions in the fractional-order system is presented, where an efficient controller is designed based on the stability theory of the discrete-time fractional-order systems. Numerical simulations are provided to validate the theoretical results derived in this research paper.

Discrete-Time Predator–Prey System Incorporating Fear Effect: Stability, Bifurcation, and Chaos Control

Discrete-Time Predator–Prey System Incorporating Fear Effect: Stability, Bifurcation, and Chaos Control

Sliding-mode-based preassigned-time control of a class of memristor chaotic systems

Abstract This paper addresses the preassigned-time chaos control problem of memristor chaotic systems with time delays. Since the introduction of memristor, the presented models are nonlinear systems with chaotic dynamics. First, the TS fuzzy method is adopted to describe the chaotic systems. Then, a sliding-model-based control approach is proposed to achieve the preassigned-time stabilization of the presented models, where the upper bound of stabilization time can be arbitrarily specified in advance. Finally, simulation results demonstrate the validity of presented control approach and theoretic results.

Memristor-coupled cubic hyperchaotic system, feedback synchronization and its application in image encryption

Discrete memristive chaotic systems play a crucial role in information security, and chaotic synchronization form the bedrock of secure and confidential communication. To enhance the chaotic complexity of the Cubic map, we introduce a memristor-coupled Cubic hyperchaotic system by integrating a discrete absolute memristor model with the Cubic map. The dynamics are thoroughly investigated through attractor phase diagrams, bifurcation diagrams, SE complexity analysis, and diagrams illustrating the distribution of dynamic behaviors. Furthermore, we establish methods for chaos control and nonlinear feedback synchronization for the memristive Cubic map. Leveraging this feedback synchronization, we achieve encrypted transmission of digital images. Simulation results validate the feasibility and robust security of the proposed encrypted transmission scheme.

Stability, bifurcation analysis and chaos control in a discrete predator–prey system incorporating prey immigration

Stability, bifurcation analysis and chaos control in a discrete predator–prey system incorporating prey immigration

Dynamical analysis, control, boundedness, and prediction for a fractional-order financial risk system

Abstract This paper delves into the dynamical analysis, chaos control, Mittag–Leffler boundedness (MLB), and forecasting a fractional-order financial risk (FOFR) system through an absolute function term. To this end, the FOFR system is first proposed, and the adomian decomposition method (ADM) is employed to resolve this fractional-order system. The stability of equilibrium points and the corresponding control schemes are assessed, and several classical tools such as Lyapunov exponents (LE), bifurcation diagrams, complexity analysis (CA), and 0–1 test are further extended to analyze the dynamical behaviors of FOFR. Then the global Mittag–Leffler attractive set (MLAS) and Mittag–Leffler positive invariant set (MLPIS) for the proposed financial risk (FR) system are discussed. Finally, a proficient reservoir-computing (RC) method is applied to forecast the temporal evolution of the complex dynamics for the proposed system, and some simulations are carried out to show the effectiveness and feasibility of the present scheme.

Nonlinear Dynamics Induced by Coil Heat in the PMDC Motor and Control

In this paper, the interesting dynamics of chaos induced by the effect of the variation of internal average heat during operation in the DC motor control by the full bridge drive are analyzed. By using simple powerful tools of analyzing nonlinear dynamical systems like phase portraits, time traces and frequency spectrum in the MATLAB-SIMULINK environment, we showed that under certain conditions, the PMDC motor develops different behaviors so as periodic limited, and chaotic attractors, when the motor drive different form of external load torque and the windings resistance variation. This paper presents the first studies on the variation of the average heat of the motor and the amplitude of the triangular load torque to produce the strange phenomena like chaos as far as our knowledge go. A chaos control of the unstable regime is proposed to stabilize the PM DC motor in a desire regime. This contribution is very important in industry because some unexplained dynamical behaviors of the DC motor driven by a full bridge now can be avoided.

A discrete fractional order cournot duopoly game model with relative profit delegation: Stability, bifurcation, chaos, 0-1 testing and control

Due to the memory effect, fractional order dynamical systems provide more realistic results compared with ordinary counterparts. In this study, we consider a Cournot-duopoly game model with relative profit delegation in the sense of Caputo fractional derivative. To describe richer dynamical behavior such as chaos in the model, a discrete dynamical system is needed. As a result of the discretization method based on the use of piecewise constant arguments, we obtain a two dimensional system of difference equations. The stability conditions of all equilibrium points of the discrete dynamical system are given comprehensively. The existence of the flip bifurcation in the system has been demonstrated theoretically. Lyapunov exponents and 0–1 test chaos imply that chaotic structures are formed as a result of this bifurcation. In addition, we present the chaos control technique such as Pyragas method to eliminate chaos in the model. All theoretical results dealing with the stability, bifurcation and chaos in the model are stimulated by numerical simulations.

Biophysical Approach to Understand Life and Cancer

ABSTRACTBackgroundFrom the perspective of biology, the characteristics of life can be categorized as cellular organizations, homeostasis, metabolism, growth, reproduction and heredity, response to stimuli and adaptation to the environment. From the perspective of physics, living organisms are highly ordered, complex, thermodynamically open systems; they are in non‐equilibrium phase. According to the second law of thermodynamics, every system in the universe is going to the disorder spontaneously. Maximum entropy signifies a thermodynamic equilibrium which means the death. Today, cancer is a major global health problem and despite the explosive development of our knowledge about the carcinogenesis the “war on cancer” has not yet been won.AimsTo examine life and cancer together based on current biophysical approach and to shed light on new paradigms.Materials & MethodsA systematic literature search for publications on a thermodynamic approach to understand life and cancer was conducted in PubMed without language restrictions. The reference lists of identified studies were also used as additional knowledge.ResultsLiving organisms exchange entropy and they gain information from the external environment. Information can be stored as memory. Life is a category of emergence like art composed from correct modules. On the contrary, cancer is the emergence of a disease formed by incorrect modules. Cancer is a chaotic disease at least for a limited period and cannot arise from healthy functional tissue units. Chaos of the lower level may be associated with the entropy increase of upper level.ConclusionsBiologic chaos control is possible.

Dynamics and control of two-dimensional discrete-time biological model incorporating weak Allee's effect.

Incorporating a weak Allee effect in a two-dimensional biological model in ℜ2, the study delves into the application of bifurcation theory, including center manifold and Ljapunov-Schmidt reduction, normal form theory, and universal unfolding, to analyze nonlinear stability issues across various engineering domains. The focus lies on the qualitative dynamics of a discrete-time system describing the interaction between prey and predator. Unlike its continuous counterpart, the discrete-time model exhibits heightened chaotic behavior. By exploring a biological Mmdel with linear functional prey response, the research elucidates the local asymptotic properties of equilibria. Additionally, employing bifurcation theory and the center manifold theorem, the analysis reveals that, for all α1 (i.e., intrinsic growth rate of prey), ð1˙ (i.e., parameter that scales the terms yn), and m (i.e., Allee effect constant), the model exhibits boundary fixed points A1 and A2, along with the unique positive fixed point A∗, given that the all parameters are positive. Additionally, stability theory is employed to explore the local dynamic characteristics, along with topological classifications, for the fixed points A1, A2, and A∗, considering the impact of the weak Allee effect on prey dynamics. A flip bifurcation is identified for the boundary fixed point A2, and a Neimark-Sacker bifurcation is observed in a small parameter neighborhood around the unique positive fixed point A∗=(mð1˙-1,α1-1-α1mð1˙-1). Furthermore, it implements two chaos control strategies, namely, state feedback and a hybrid approach. The effectiveness of these methods is demonstrated through numerical simulations, providing concrete illustrations of the theoretical findings. The model incorporates essential elements of population dynamics, considering interactions such as predation, competition, and environmental factors, along with a weak Allee effect influencing the prey population.

Hybrid adaptive moment estimation based performance measure approach for complex reliability-based design optimization

The complexity of engineering problems often poses challenges, especially in reliability-based design optimization, where the nonlinearity of the performance function is not known in advance. The substantial costs and oscillating results significantly impede the engineering application for highly nonlinear problems. To address this issue, a hybrid adaptive moment estimation (HAME) method is proposed in this work. Given that the performance measure approach is heavily influenced by the gradient of performance function, this method employs the statistical moment information of the gradient, thereby accelerating the search for the minimum performance target point. By combining gradient mean and modified chaos control as new search directions, oscillation phenomena are resolved. To filter the aggregated gradient calculations, the gradient variance and state variable are introduced to approximate the gradients for weakly nonlinear performance functions or in later iterations by the dynamic identification of the nonlinearity of the performance function. The proposed method eliminates the limitation of taking the upper bound for the chaos control factor and addresses the balance issue between efficiency and robustness. The advantages of the proposed method are demonstrated through inverse reliability analysis problems, several highly nonlinear classic RBDO examples, and engineering applications of the crank rod mechanism of an engine.

Dynamic Analysis of the Multichannel Supply Chain Under Carbon Subsidy Policy

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.

Free-will arbitrary time adaptive chaos control for permanent magnet synchronous motor

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.

A class of memristive Hénon maps

Abstract Memristor, the electronic component, is introduced in the Hénon map and is studied extensively. Several chaotic maps are proposed by constructing the memristors through nonlinear functions such as absolute value functions, trigonometric functions, and activation functions. It is found that in a part of the proposed chaotic maps, the local offset boosting of the system variable can be guided by a single parameter. Not only that, the generation of homogeneous multistability can be controlled by the initial conditions of the systems. Moreover, the number of homogeneous attractors produced changes when the system parameters are varied. In addition, the control of chaos can be achieved by adjusting the excitation frequency of the memristor. The theoretical results and numerical laws presented in this paper are verified by circuit implementation based on the microcontroller unit.

Complex dynamical properties and chaos control for a discrete modified Leslie-Gower prey-predator system with Holling II functional response

In this study, the semi-discretization technique is employed to establish a discrete representation of a modified Leslie-Gower prey-predator system that includes a Holling II type functional response. The dynamics of this model are then analyzed through the application of center manifold theory and bifurcation theory. We present comprehensive results for the local stability of the fixed points across the entire parameter space. Additionally, we provide sufficient conditions for the occurrence of flip bifurcation and Neimark-Sacker bifurcation. Besides, the system has experienced a flip bifurcation to chaos controlled using the method of chaos control, viz., state feedback method, pole placement technique, and hybrid control strategy. Furthermore, we provide specific conditions to ensure that bifurcation and chaos can be stabilized. Finally, numerical simulations are conducted to validate theoretical analysis and illustrate several new complex dynamical behaviors between two species.