Dynamical analysis, circuit implementation and synchronization of a new memristive hyperchaotic system with coexisting attractors

2021 ◽  
pp. 2150187
Author(s):  
Qiang Lai ◽  
Zhiqiang Wan ◽  
Paul Didier Kamdem Kuate ◽  
Hilaire Fotsin
Keyword(s):  
Analog Circuit ◽  
Sufficient Conditions ◽  
Dynamical Analysis ◽  
Control Technique ◽  
Hyperchaotic System ◽  
Experimental Implementation ◽  
Memristive System ◽  
Theoretical And Numerical Analysis ◽  
Jerk System ◽  
Two Equilibria

This paper constructs a novel memristive hyperchaotic system by introducing the flux-controlled memristor to an extended jerk system. The memristive system has two equilibria and coexists two symmetric hyperchaotic attractors. The dynamic behaviors of the system are studied through bifurcation analysis. The analog circuit design and microcontroller-based experimental implementation of the system are presented. The synchronization of the system is realized by using the adaptive control technique. The sufficient conditions for synchronization are established via theoretical and numerical analysis.

scholarly journals Dynamical analysis of a giving up smoking model with time delay

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Zizhen Zhang ◽  
Ruibin Wei ◽  
Wanjun Xia
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Local Stability ◽  
Center Manifold ◽  
Dynamical Behavior ◽  
Sufficient Conditions ◽  
Dynamical Analysis ◽  
Normal Form Theory ◽  
Center Manifold Theorem ◽  
Form Theory

AbstractIn this paper, we are concerned with a delayed smoking model in which the population is divided into five classes. Sufficient conditions guaranteeing the local stability and existence of Hopf bifurcation for the model are established by taking the time delay as a bifurcation parameter and employing the Routh–Hurwitz criteria. Furthermore, direction and stability of the Hopf bifurcation are investigated by applying the center manifold theorem and normal form theory. Finally, computer simulations are implemented to support the analytic results and to analyze the effects of some parameters on the dynamical behavior of the model.

scholarly journals Fuzzy Stabilization for Nonlinear Discrete Ship Steering Stochastic Systems Subject to State Variance and Passivity Constraints

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Wen-Jer Chang ◽  
Bo-Jyun Huang ◽  
Po-Hsun Chen
Keyword(s):  
Linear Matrix Inequality ◽  
Discrete Time ◽  
Stochastic Systems ◽  
Fuzzy Controller ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Control Technique ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Ship Steering

For nonlinear discrete-time stochastic systems, a fuzzy controller design methodology is developed in this paper subject to state variance constraint and passivity constraint. According to fuzzy model based control technique, the nonlinear discrete-time stochastic systems considered in this paper are represented by the discrete-time Takagi-Sugeno fuzzy models with multiplicative noise. Employing Lyapunov stability theory, upper bound covariance control theory, and passivity theory, some sufficient conditions are derived to find parallel distributed compensation based fuzzy controllers. In order to solve these sufficient conditions, an iterative linear matrix inequality algorithm is applied based on the linear matrix inequality technique. Finally, the fuzzy stabilization problem for nonlinear discrete ship steering stochastic systems is investigated in the numerical example to illustrate the feasibility and validity of proposed fuzzy controller design method.

Research on cyber-physical system control strategy under false data injection attack perception

2022 ◽  
pp. 014233122110693
Author(s):  
Zhiwen Wang ◽  
Bin Zhang ◽  
Xiangnan Xu ◽  
Usman ◽  
Long Li
Keyword(s):  
Control Strategy ◽  
Physical System ◽  
Sufficient Conditions ◽  
Switched System ◽  
Lyapunov Methods ◽  
Control Technique ◽  
Cyber Physical System ◽  
Time Data ◽  
False Data Injection ◽  
Injection Attacks

This paper investigates the security control problem of the cyber-physical system under false data injection attacks. A model predictive switching control strategy based on attack perception is proposed to compensate for the untrusted sequence of data caused by false data injection attacks. First, the binary attack detector is applied whether the system has suffered the attack. If the attack occurs, multistep correction is carried out for the future data according to the previous time data, and the waiting period [Formula: see text] is set. The input and output sequence of the controller is reconstructed, and the system is modeled as a constant time-delay switched system. Subsequently, the Lyapunov methods and average-dwell time are combined to provide sufficient conditions for the asymptotical stability of closed-loop switched system. Finally, the simulation of the networked first-order inverted pendulum model reveals that the control technique can efficiently suppress the influence of the attacks.

An exponential jerk system, its fractional-order form with dynamical analysis and engineering application

2019 ◽  
Vol 24 (10) ◽  
pp. 7469-7479 ◽  
Author(s):  
Karthikeyan Rajagopal ◽  
Akif Akgul ◽  
Sajad Jafari ◽  
Anitha Karthikeyan ◽  
Unal Cavusoglu ◽  
...  
Keyword(s):  
Fractional Order ◽  
Engineering Application ◽  
Dynamical Analysis ◽  
Order Form ◽  
Jerk System

Dynamical Analysis and Circuit Simulation of a New Fractional-Order Hyperchaotic System and Its Discretization

2016 ◽  
Vol 26 (13) ◽  
pp. 1650222 ◽  
Author(s):  
A. M. A. El-Sayed ◽  
A. Elsonbaty ◽  
A. A. Elsadany ◽  
A. E. Matouk
Keyword(s):  
Fractional Order ◽  
Initial Conditions ◽  
Circuit Simulation ◽  
Equilibrium Points ◽  
Dynamical Behavior ◽  
Phase Portraits ◽  
Control Technique ◽  
Order System ◽  
Qualitative Behavior ◽  
Hyperchaotic System

This paper presents an analytical framework to investigate the dynamical behavior of a new fractional-order hyperchaotic circuit system. A sufficient condition for existence, uniqueness and continuous dependence on initial conditions of the solution of the proposed system is derived. The local stability of all the system’s equilibrium points are discussed using fractional Routh–Hurwitz test. Then the analytical conditions for the existence of a pitchfork bifurcation in this system with fractional-order parameter less than 1/3 are provided. Conditions for the existence of Hopf bifurcation in this system are also investigated. The dynamics of discretized form of our fractional-order hyperchaotic system are explored. Chaos control is also achieved in discretized system using delay feedback control technique. The numerical simulation are presented to confirm our theoretical analysis via phase portraits, bifurcation diagrams and Lyapunov exponents. A text encryption algorithm is presented based on the proposed fractional-order system. The results show that the new system exhibits a rich variety of dynamical behaviors such as limit cycles, chaos and transient phenomena where fractional-order derivative represents a key parameter in determining system qualitative behavior.

scholarly journals Robust Impulsive Stabilization of Uncertain Nonlinear Singular Systems with Application to Transportation Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-4 ◽  
Author(s):  
Shaohong Fang
Keyword(s):  
Impulsive Control ◽  
Singular Systems ◽  
Singular System ◽  
Sufficient Conditions ◽  
Transportation Systems ◽  
Control Technique ◽  
Asymptotically Stable ◽  
Matrix Inequalities ◽  
Stabilization Problem ◽  
Uncertain Singular Systems

We consider the robust asymptotical stabilization problem for uncertain singular systems. We design a new impulsive control technique to ensure that the controlled singular system is robustly asymptotically stable and hence derive the corresponding stability criteria. These sufficient conditions are expressed in the form of algebra matrix inequalities and can be implemented numerically. We finally provide a numerical example of a transportation system to illustrate the effectiveness and usefulness of the proposed criteria.

scholarly journals Hybrid State Variable Incremental Integral for Reconstructing Extreme Multistability in Memristive Jerk System with Cubic Nonlinearity

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-16 ◽  
Author(s):  
Mo Chen ◽  
Yang Feng ◽  
Han Bao ◽  
Bocheng Bao ◽  
Huagan Wu ◽  
...  
Keyword(s):  
Integral Transformation ◽  
Equilibrium Points ◽  
Mechanism Analysis ◽  
State Variables ◽  
Cubic Nonlinearity ◽  
Hybrid State ◽  
State Variable ◽  
Extreme Multistability ◽  
Memristive System ◽  
Jerk System

Memristive system with infinitely many equilibrium points has attracted much attention for the generation of extreme multistability, whose initial-dependent dynamics can be interpreted in a reduced-order model through incremental integral transformation of state variables. But, the memristive system with any extra nonlinear terms besides the memristor ones cannot be handled directly using this method. In addition, the transformed state variables could be divergent due to the asymmetry of the original system. To solve these problems, a hybrid state variable incremental integral (HSVII) method is proposed in this paper. With this method, the extreme multistability in a four-dimensional (4D) memristive jerk system with cubic nonlinearity is successfully reconstituted in a three-dimensional (3D) model and the divergent state variables are eliminated through ingenious linear state variable mapping. Thus, mechanism analysis and physical control of the special extreme multistability can readily be performed. A hardware circuit is finally designed and fabricated, and the theoretical and numerical results are verified by the experimental measurements. It is demonstrated that this HSVII method is effective for the analysis of multistable system with high-order nonlinearities.

A New 4D Four-Wing Memristive Hyperchaotic System: Dynamical Analysis, Electronic Circuit Design, Shape Synchronization and Secure Communication

2020 ◽  
Vol 30 (10) ◽  
pp. 2050147 ◽  
Author(s):  
Fei Yu ◽  
Shuai Qian ◽  
Xi Chen ◽  
Yuanyuan Huang ◽  
Li Liu ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Secure Communication ◽  
Electronic Circuit ◽  
Mathematical Structure ◽  
Dynamical Analysis ◽  
Hyperchaotic System ◽  
Chen System ◽  
Information Signal ◽  
Communication Scheme ◽  
Good Agreement

In this paper, a simple four-wing chaotic attractor is first proposed by replacing the constant parameters of the Chen system with a periodic piecewise function. Then, a new 4D four-wing memristive hyperchaotic system is presented by adding a flux-controlled memristor with linear memductance into the proposed four-wing Chen system. The memristor mathematical structure model is simple and easy to implement. Dynamical analysis and numerical simulation of the memristive hyperchaotic system are carried out. Then, the electronic circuit of the hyperchaotic system is designed and implemented. The results of numerical simulation are in good agreement with the electronic circuit experiment. In addition, shape synchronization control for the 4D four-wing memristive hyperchaotic system is realized, and a communication system is designed by using the shape synchronization method. Finally, secure signal masking application is implemented on Matlab platform. In the developed secure communication scheme, the information signal overlaps with the chaotic masking signal, which improves the security of the system.

scholarly journals A Novel Hypogenetic Chaotic Jerk System: Modeling, Circuit Implementation, and Its Application

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Jiancheng Liu ◽  
Karthikeyan Rajagopal ◽  
Tengfei Lei ◽  
Sezgin Kaçar ◽  
Burak Arıcıoğlu ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Electronic Circuit ◽  
Random Number ◽  
System Modeling ◽  
Random Number Generator ◽  
Superior Performance ◽  
Dynamical Analysis ◽  
Number Generator ◽  
Circuit Implementation ◽  
Jerk System

When revising the polarity and amplitude information in the feedback, a unique hypogenetic jerk system was obtained which has two controllers to switch the equilibria between stable and unstable. After providing some basic dynamical analysis, an electronic circuit was implemented, and the phase trajectory in the oscilloscope agrees with the numerical simulation. Further exploration shows that this unique chaotic system has superior performance as a random number generator or in voice encryption application.

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