scholarly journals A Symmetric Controllable Hyperchaotic Hidden Attractor

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 550 ◽  
Author(s):  
Xin Zhang ◽  
Chunbiao Li ◽  
Tengfei Lei ◽  
Zuohua Liu ◽  
Changyuan Tao
Keyword(s):  
Numerical Simulation ◽  
Chaotic System ◽  
Hidden Attractor ◽  
Theoretic Analysis ◽  
Free System ◽  
Simple Feedback

By introducing a simple feedback, a hyperchaotic hidden attractor is found in the newly proposed Lorenz-like chaotic system. Some variables of the equilibria-free system can be controlled in amplitude and offset by an independent knob. A circuit experiment based on Multisim is consistent with the theoretic analysis and numerical simulation.

scholarly journals Dynamic Analysis and Robust Control of a Chaotic System with Hidden Attractor

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Huaigu Tian ◽  
Zhen Wang ◽  
Peijun Zhang ◽  
Mingshu Chen ◽  
Yang Wang
Keyword(s):  
Numerical Simulation ◽  
Robust Control ◽  
Theoretical Analysis ◽  
Chaotic System ◽  
Finite Time ◽  
Original System ◽  
Slave System ◽  
Hidden Attractor ◽  
Time Stability ◽  
Finite Time Stability

In this paper, a 3D jerk chaotic system with hidden attractor was explored, and the dissipativity, equilibrium, and stability of this system were investigated. The attractor types, Lyapunov exponents, and Poincare section of the system under different parameters were analyzed. Additionally, a circuit was carried out, and a good similarity between the circuit experimental results and the theoretical analysis testifies the feasibility and practicality of the original system. Furthermore, a robust feedback controller was designed based on the finite-time stability theory, which guarantees the synchronization of 3D jerk master-slave system in finite time and asymptotically converges to the origin. Finally, we also give verification for the discussion in this paper by numerical simulation.

Nonlinear Dynamics and Application of the Four Dimensional Autonomous Hyper-Chaotic System

2014 ◽  
Author(s):  
Ge Kai ◽  
Wei Zhang
Keyword(s):  
Nonlinear Dynamics ◽  
Numerical Simulation ◽  
Differential Equations ◽  
Chaotic System ◽  
Dynamical Behavior ◽  
Three Dimensional ◽  
Phase Portraits ◽  
State Variables ◽  
Chaotic Motions ◽  
Finance System

In this paper, we establish a dynamic model of the hyper-chaotic finance system which is composed of four sub-blocks: production, money, stock and labor force. We use four first-order differential equations to describe the time variations of four state variables which are the interest rate, the investment demand, the price exponent and the average profit margin. The hyper-chaotic finance system has simplified the system of four dimensional autonomous differential equations. According to four dimensional differential equations, numerical simulations are carried out to find the nonlinear dynamics characteristic of the system. From numerical simulation, we obtain the three dimensional phase portraits that show the nonlinear response of the hyper-chaotic finance system. From the results of numerical simulation, it is found that there exist periodic motions and chaotic motions under specific conditions. In addition, it is observed that the parameter of the saving has significant influence on the nonlinear dynamical behavior of the four dimensional autonomous hyper-chaotic system.

scholarly journals Low Model Analysis and Synchronous Simulation of the Wave Mechanics

2016 ◽  
Vol 2016 ◽  
pp. 1-13
Author(s):  
Wenyuan Duan ◽  
Heyuan Wang ◽  
Meng Kan
Keyword(s):  
Numerical Simulation ◽  
Lyapunov Function ◽  
Chaotic System ◽  
Invariant Set ◽  
Positive Definite ◽  
Chaotic Attractors ◽  
Wave Mechanics ◽  
Wave Dynamics ◽  
Simulation Results ◽  
Positive Invariant Set

The dynamic behavior of a chaotic system in the internal wave dynamics and the problem of the tracing and synchronization are investigated, and the numerical simulation is carried out in this paper. The globally exponentially attractive set and positive invariant set of the chaotic system are studied via constructing the positive definite and radial unbounded Lyapunov function. There are no equilibrium positions, periodic solutions, quasi-period motions, wandering recovering motions, and other chaotic attractors of the system out of the globally exponentially attractive set. Strange attractors can only locate in the globally exponentially attractive set. A feedback controller is designed for the chaotic system to realize the control of the unstable point. The second method of Lyapunov is used to discuss theoretically the rationality of the design of the controller. The driving-response synchronization method is used to realize the globally exponential synchronization. The numerical simulation is carried out by MATLAB software, and the simulation results show that the method is effective.

Various Types of Coexisting Attractors in a New 4D Autonomous Chaotic System

2017 ◽  
Vol 27 (09) ◽  
pp. 1750142 ◽  
Author(s):  
Qiang Lai ◽  
Akif Akgul ◽  
Xiao-Wen Zhao ◽  
Huiqin Pei
Keyword(s):  
Numerical Simulation ◽  
Dynamic Behavior ◽  
Chaotic System ◽  
Limit Cycles ◽  
Electronic Circuit ◽  
Strange Attractors ◽  
Bifurcation Diagrams ◽  
Coexisting Attractors ◽  
Signum Function ◽  
Multiple Coexisting Attractors

An unique 4D autonomous chaotic system with signum function term is proposed in this paper. The system has four unstable equilibria and various types of coexisting attractors appear. Four-wing and four-scroll strange attractors are observed in the system and they will be broken into two coexisting butterfly attractors and two coexisting double-scroll attractors with the variation of the parameters. Numerical simulation shows that the system has various types of multiple coexisting attractors including two butterfly attractors with four limit cycles, two double-scroll attractors with a limit cycle, four single-scroll strange attractors, four limit cycles with regard to different parameters and initial values. The coexistence of the attractors is determined by the bifurcation diagrams. The chaotic and hyperchaotic properties of the attractors are verified by the Lyapunov exponents. Moreover, we present an electronic circuit to experimentally realize the dynamic behavior of the system.

Theoretic analysis and numerical simulation of metal two-sided multipactor discharge

2011 ◽  
Vol 23 (2) ◽  
pp. 454-462
Author(s):  
董烨 Dong Ye ◽  
董志伟 Dong Zhiwei ◽  
杨温渊 Yang Wenyuan
Keyword(s):  
Numerical Simulation ◽  
Theoretic Analysis ◽  
Multipactor Discharge

scholarly journals Modelling and circuit realisation of a new no-equilibrium chaotic system with hidden attractor and coexisting attractors

2020 ◽  
Vol 56 (20) ◽  
pp. 1044-1046 ◽  
Author(s):  
Qiang Lai ◽  
Zhiqiang Wan ◽  
Paul Didier Kamdem Kuate
Keyword(s):  
Chaotic System ◽  
Hidden Attractor ◽  
Coexisting Attractors

A New Dynamic System Analysis

2013 ◽  
Vol 392 ◽  
pp. 222-226
Author(s):  
Bao Liang Mi ◽  
Guo Zeng Wu
Keyword(s):  
Numerical Simulation ◽  
Theoretical Analysis ◽  
Dynamic System ◽  
Bifurcation Diagram ◽  
Chaotic System ◽  
System Analysis ◽  
Electronic Circuit ◽  
Circuit Implementation ◽  
Dynamical Properties ◽  
Electronic Circuit Implementation

A new four-dimensional chaotic system is presented in this paper. Some basic dynamical Properties of this chaotic system are investigated by means of Poincaré mapping, Lyapunov exponents and bifurcation diagram. The dynamical behaviours of this system are proved not only by performing numerical simulation and brief theoretical analysis but also by conducting an electronic circuit implementation.

Memristor Oscillators and its FPGA Implementation

2011 ◽  
Vol 383-390 ◽  
pp. 6992-6997 ◽  
Author(s):  
Ai Xue Qi ◽  
Cheng Liang Zhang ◽  
Guang Yi Wang
Keyword(s):  
Numerical Simulation ◽  
Chaotic System ◽  
Field Programmable Gate Array ◽  
Chaotic Attractor ◽  
Hardware Implementation ◽  
Fpga Implementation ◽  
Experimental Results ◽  
Linear Resistance ◽  
Non Linear ◽  
Field Programmable

This paper presents a method that utilizes a memristor to replace the non-linear resistance of typical Chua’s circuit for constructing a chaotic system. The improved circuit is numerically simulated in the MATLAB condition, and its hardware implementation is designed using field programmable gate array (FPGA). Comparing the experimental results with the numerical simulation, the two are the very same, and be able to generate chaotic attractor.

scholarly journals A Luenberger-Like Observer for Multistable Kapitaniak Chaotic System

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
J. Humberto Pérez-Cruz ◽  
Jacobo Marcos Allende Peña ◽  
Christian Nwachioma ◽  
Jose de Jesus Rubio ◽  
Jaime Pacheco ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Chaotic System ◽  
Estimation Error ◽  
Lipschitz Constant ◽  
Experimental Results ◽  
Good Agreement

The objective of this paper is to estimate the unmeasurable variables of a multistable chaotic system using a Luenberger-like observer. First, the observability of the chaotic system is analyzed. Next, a Lipschitz constant is determined on the attractor of this system. Then, the methodology proposed by Raghavan and the result proposed by Thau are used to try to find an observer. Both attempts are unsuccessful. In spite of this, a Luenberger-like observer can still be used based on a proposed gain. The performance of this observer is tested by numerical simulation showing the convergence to zero of the estimation error. Finally, the chaotic system and its observer are implemented using 32-bit microcontrollers. The experimental results confirm good agreement between the responses of the implemented and simulated observers.

Sign in / Sign up

Export Citation Format

Share Document