A new family of 5D, 6D, 7D and 8D hyperchaotic systems from the 4D hyperchaotic Vaidyanathan system, the dynamic analysis of the 8D hyperchaotic system with six positive Lyapunov exponents and an application to secure communication design

2020 ◽  
Vol 35 (3) ◽  
pp. 241
Author(s):  
Sundarapandian Vaidyanathan ◽  
Mustak E. Yalcin ◽  
Toufik Bouden ◽  
Khaled Benkouider
Keyword(s):  
Dynamic Analysis ◽  
Lyapunov Exponents ◽  
Secure Communication ◽  
Hyperchaotic System ◽  
Communication Design ◽  
New Family ◽  
Hyperchaotic Systems

scholarly journals Constructing Discrete Chaotic Systems with Positive Lyapunov Exponents

2018 ◽  
Vol 28 (07) ◽  
pp. 1850084 ◽  
Author(s):  
Chuanfu Wang ◽  
Chunlei Fan ◽  
Qun Ding
Keyword(s):  
Lyapunov Exponents ◽  
Chaotic System ◽  
Secure Communication ◽  
Discrete System ◽  
Chaotic Systems ◽  
Hyperchaotic System ◽  
Universal Method ◽  
Periodic Attractors ◽  
Chaotic Secure Communication ◽  
Hyperchaotic Systems

The chaotic system is widely used in chaotic cryptosystem and chaotic secure communication. In this paper, a universal method for designing the discrete chaotic system with any desired number of positive Lyapunov exponents is proposed to meet the needs of hyperchaotic systems in chaotic cryptosystem and chaotic secure communication, and three examples of eight-dimensional discrete system with chaotic attractors, eight-dimensional discrete system with fixed point attractors and eight-dimensional discrete system with periodic attractors are given to illustrate how the proposed methods control the Lyapunov exponents. Compared to the previous methods, the positive Lyapunov exponents are used to reconstruct a hyperchaotic system.

scholarly journals Dynamic Analysis and Circuit Design of a Novel Hyperchaotic System with Fractional-Order Terms

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Abir Lassoued ◽  
Olfa Boubaker
Keyword(s):  
Dynamic Analysis ◽  
Circuit Design ◽  
Fractional Order ◽  
Potential Application ◽  
Complex Dynamics ◽  
Equilibrium Points ◽  
Hyperchaotic System ◽  
Software Simulation ◽  
Simulation Results ◽  
Hyperchaotic Systems

A novel hyperchaotic system with fractional-order (FO) terms is designed. Its highly complex dynamics are investigated in terms of equilibrium points, Lyapunov spectrum, and attractor forms. It will be shown that the proposed system exhibits larger Lyapunov exponents than related hyperchaotic systems. Finally, to enhance its potential application, a related circuit is designed by using the MultiSIM Software. Simulation results verify the effectiveness of the suggested circuit.

scholarly journals Adaptive Multi-Switching Synchronization of High-Order Memristor-Based Hyperchaotic System with Unknown Parameters and Its Application in Secure Communication

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-18 ◽  
Author(s):  
Zhili Xiong ◽  
Shaocheng Qu ◽  
Jing Luo
Keyword(s):  
Numerical Simulation ◽  
Secure Communication ◽  
High Order ◽  
Hyperchaotic System ◽  
Uncertain Parameters ◽  
Unknown Parameters ◽  
Switching Controller ◽  
Simulation Results ◽  
Hyperchaotic Systems ◽  
True Values

This article investigates an adaptive multi-switching synchronization for two identical high-order memristor-based hyperchaotic systems with uncertain parameters. Firstly, the dynamic characteristics of two high-order memristor hyperchaotic systems with uncertain parameters are analyzed. Then, an adaptive multi-switching controller is designed to realize the multi-switching synchronization of the two high-order hyperchaotic systems, and the unknown parameters of the systems are identified to their true values. Furthermore, numerical simulation results testify the effectiveness of the proposed strategy. Finally, the proposed algorithm applied in secure communication of masking encryption and image encryption is validated by statistical analysis.

scholarly journals Synchronization for a Class of Fractional-Order Hyperchaotic System and Its Application

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Wen Tan ◽  
Feng Ling Jiang ◽  
Chuang Xia Huang ◽  
Lan Zhou
Keyword(s):  
Theoretical Analysis ◽  
Fractional Order ◽  
Secure Communication ◽  
Controller Design ◽  
Design Method ◽  
Hyperchaotic System ◽  
Response System ◽  
Control Scheme ◽  
The Stability ◽  
Hyperchaotic Systems

A new controller design method is proposed to synchronize the fractional-order hyperchaotic system through the stability theory of fractional calculus; the synchronization between two identical fractional-order Chen hyperchaotic systems is realized by designing only two suitable controllers in the response system. Furthermore, this control scheme can be used in secure communication via the technology of chaotic masking using the complex nonperiodic information as trial message, and the useful information can be recovered at the receiver. Numerical simulations coincide with the theoretical analysis.

Constructing Higher-Dimensional Nondegenerate Hyperchaotic Systems with Multiple Controllers

2017 ◽  
Vol 27 (09) ◽  
pp. 1750146 ◽  
Author(s):  
Jianbin He ◽  
Simin Yu ◽  
Jinhu Lü
Keyword(s):  
Lyapunov Exponents ◽  
Hyperchaotic System ◽  
Positive Real ◽  
Controlled System ◽  
New Approach ◽  
Maximum Value ◽  
Asymptotic Stable ◽  
Higher Dimensional ◽  
Hyperchaotic Systems ◽  
Multiple Controllers

This paper proposes a new approach for constructing higher-dimensional nondegenerate hyperchaotic system with multiple controllers. Here, the so-called higher-dimensional nondegenerate hyperchaotic system means that it can be provided with a maximum number of positive Lyapunov exponents, which has been an open problem for research in recent years. The details of design are given by three steps as follows: (i) Design an [Formula: see text]-dimensional nominal matrix and similarity transformation matrix, and get an asymptotic stable nominal system; (ii) Add a master controller for the nominal matrix and get the controlled system. Then, find suitable control positions such that the controlled system satisfies the average eigenvalue criterion, i.e. the number of average eigenvalues with positive real parts of all Jacobi matrices over a given period of time is equal to ([Formula: see text]), and the maximum value of average eigenvalues with positive real parts is greater than a given threshold [Formula: see text]; (iii) Add nonmaster controllers, and the control positions are fixed and parameters are given in advance. So it can generate nondegenerate hyperchaotic systems with ([Formula: see text]) positive Lyapunov exponents. Finally, two typical examples are given to show the feasibility and effectiveness of the proposed method.

Construction of Higher-Dimensional Hyperchaotic Systems with a Maximum Number of Positive Lyapunov Exponents under Average Eigenvalue Criteria

2019 ◽  
Vol 28 (09) ◽  
pp. 1950151
Author(s):  
Jianbin He ◽  
Simin Yu
Keyword(s):  
Lyapunov Exponents ◽  
Equilibrium Points ◽  
Control Period ◽  
Threshold Value ◽  
Hyperchaotic System ◽  
Positive Real ◽  
Controlled System ◽  
Number Formula ◽  
And Performance ◽  
Hyperchaotic Systems

Over the last 40 years, the design of [Formula: see text]-dimensional hyperchaotic systems with a maximum number ([Formula: see text]) of positive Lyapunov exponents has been an open problem for research. Nowadays it is not difficult to design [Formula: see text]-dimensional hyperchaotic systems with less than ([Formula: see text]) positive Lyapunov exponents, but it is still extremely difficult to design an [Formula: see text]-dimensional hyperchaotic system with the maximum number ([Formula: see text]) of positive Lyapunov exponents. This paper aims to resolve this challenging problem by developing a chaotification approach using average eigenvalue criteria. The approach consists of four steps: (i) a globally bounded controlled system is designed based on an asymptotically stable nominal system with a uniformly bounded controller; (ii) a closed-loop pole assignment technique is utilized to ensure that the numbers of eigenvalues with positive real parts of the controlled system be equal to ([Formula: see text]) and ([Formula: see text]), respectively, at two saddle-focus equilibrium points; (iii) the number of average eigenvalues with positive real parts is ensured to be equal to ([Formula: see text]) for the controlled system over a given control period; (iv) the smallest value of the positive real parts of the average eigenvalues is ensured to be greater than a given threshold value. Finally, the paper is closed with some typical examples which illustrate the feasibility and performance of the proposed design methodology.

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