Finite-time complex function synchronization of multiple complex-variable chaotic systems with network transmission and combination mode

2018 ◽  
Vol 24 (22) ◽  
pp. 5461-5471 ◽  
Author(s):  
Xiangyong Chen ◽  
Jinde Cao ◽  
Ju H Park ◽  
Guangdeng Zong ◽  
Jianlong Qiu
Keyword(s):  
Complex Variable ◽  
Finite Time ◽  
Chaotic Systems ◽  
Simulation Analysis ◽  
Complex Function ◽  
Finite Time Stability ◽  
Detailed Simulation ◽  
Synchronization Mechanisms ◽  
Combination Mode ◽  
Function Synchronization

Two kinds of finite-time complex function synchronization for multiple complex-variable chaotic systems are investigated. Both the transmission mode and combination mode are respectively considered. By considering complex functions as the scaling factors, the definitions of the two different synchronization mechanisms are established, and the appropriate schemes are proposed to guarantee the finite-time stability of all error systems. Furthermore, two verifiable criteria are derived to synchronize multi-systems. Finally, detailed simulation analysis is provided to validate the effectiveness of all innovations.

FINITE-TIME SYNCHRONIZATION OF DYNAMICAL NETWORKS COUPLED WITH COMPLEX-VARIABLE CHAOTIC SYSTEMS

2013 ◽  
Vol 24 (09) ◽  
pp. 1350058 ◽  
Author(s):  
ZHAOYAN WU ◽  
QINGLING YE ◽  
DANFENG LIU
Keyword(s):  
Complex Variable ◽  
Finite Time ◽  
Function Method ◽  
Chaotic Systems ◽  
Time Synchronization ◽  
Sufficient Conditions ◽  
Time Stability ◽  
Dynamical Networks ◽  
Finite Time Stability ◽  
Lyapunov Function Method

In this paper, finite-time synchronization of dynamical networks coupled with complex-variable chaotic systems is investigated. According to Lyapunov function method and finite-time stability theory, both the dynamical networks without and with coupling delay are considered through designing proper finite-time controllers. Several sufficient conditions for finite-time synchronization are derived and verified to be effective by some numerical examples.

scholarly journals Finite Time Synchronization for Fractional Order Sprott C Systems with Hidden Attractors

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
Cui Yan ◽  
He Hongjun ◽  
Lu Chenhui ◽  
Sun Guan
Keyword(s):  
Fractional Order ◽  
Finite Time ◽  
Chaotic Systems ◽  
Time Synchronization ◽  
Engineering Practice ◽  
Fractional Order Systems ◽  
Spectral Entropy ◽  
Hidden Attractors ◽  
Finite Time Stability ◽  
Peculiar Phenomenon

Fractional order systems have a wider range of applications. Hidden attractors are a peculiar phenomenon in nonlinear systems. In this paper, we construct a fractional-order chaotic system with hidden attractors based on the Sprott C system. According to the Adomain decomposition method, we numerically simulate from several algorithms and study the dynamic characteristics of the system through bifurcation diagram, phase diagram, spectral entropy, and C0 complexity. The results of spectral entropy and C0 complexity simulations show that the system is highly complex. In order to apply such research results to engineering practice, for such fractional-order chaotic systems with hidden attractors, we design a controller to synchronize according to the finite-time stability theory. The simulation results show that the synchronization time is short and the robustness is stable. This paper lays the foundation for the study of fractional order systems with hidden attractors.

scholarly journals Finite Time Stability of Finance Systems with or without Market Confidence Using Less Control Input

2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Chao Ma ◽  
Yujuan Tian ◽  
Zhongfeng Qu
Keyword(s):  
Finite Time ◽  
Chaotic Systems ◽  
Control Method ◽  
Control Input ◽  
Three Dimension ◽  
Time Stability ◽  
Finance System ◽  
Finite Time Stability ◽  
Single Controller ◽  
Simulation Results

In this paper, we make an exploration of a technique to control a class of finance chaotic systems. This technique allows one to achieve the finite time stability of the finance system more effectively with less control input energy. First, the finite time stability of three dimension finance system without market confidence is analyzed by using a single controller. Then, two controllers are designed to stabilize the four-dimension finance system with market confidence. Moreover, the finite time stability of the three-dimension and four-dimension finance system with unknown parameter is also studied. Finally, simulation results are presented to show the chaotic behaviour of the finance systems, verify the effectiveness of the proposed control method, and illustrate its advantages compared with other methods.

Hidden Chaotic Attractors and Synchronization for a New Fractional-Order Chaotic System

2019 ◽  
Vol 14 (8) ◽  
Author(s):  
Zuoxun Wang ◽  
Jiaxun Liu ◽  
Fangfang Zhang ◽  
Sen Leng
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Finite Time ◽  
Chaotic Systems ◽  
Time Synchronization ◽  
Chaotic Attractors ◽  
Finite Time Stability ◽  
Integer Order ◽  
Different Types ◽  
Synchronization Scheme

Although a large number of hidden chaotic attractors have been studied in recent years, most studies only refer to integer-order chaotic systems and neglect the relationships among chaotic attractors. In this paper, we first extend LE1 of sprott from integer-order chaotic systems to fractional-order chaotic systems, and we add two constant controllers which could produce a novel fractional-order chaotic system with hidden chaotic attractors. Second, we discuss its complicated dynamic characteristics with the help of projection pictures and bifurcation diagrams. The new fractional-order chaotic system can exhibit self-excited attractor and three different types of hidden attractors. Moreover, based on fractional-order finite time stability theory, we design finite time synchronization scheme of this new system. And combination synchronization of three fractional-order chaotic systems with hidden chaotic attractors is also derived. Finally, numerical simulations demonstrate the effectiveness of the proposed synchronization methods.

scholarly journals Fuzzy Finite-Time Stability of Chaotic Systems with Time-Varying Delay and Parameter Uncertainties

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Dong Li ◽  
Jinde Cao
Keyword(s):  
Finite Time ◽  
Chaotic Systems ◽  
Time Varying ◽  
Time Stability ◽  
Parameter Uncertainties ◽  
New Model ◽  
Finite Time Stability ◽  
Time Varying Delay ◽  
S Model ◽  
Varying Delay

This paper discusses the finite-time stability of chaotic systems with time-varying delay and parameter uncertainties. A new model based on Takagi-Sugeno (T-S) model is proposed for representing chaotic systems. By the new model, finite-time stability of chaotic systems can be converted into stabilization of fuzzy T-S systems with parameter uncertainties. A sufficient condition is given in terms of matrix inequalities, which guarantees the finite-time stability for fuzzy systems can be achieved. Numerical simulations on the chaotic systems are presented to demonstrate the effectiveness of the theoretical results.

Robust Finite-Time Stabilization of Fractional-Order Chaotic Systems based on Fractional Lyapunov Stability Theory

2012 ◽  
Vol 7 (2) ◽  
Author(s):  
Mohammad Pourmahmood Aghababa
Keyword(s):  
Fractional Order ◽  
Lyapunov Stability ◽  
Finite Time ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Control Method ◽  
Lyapunov Stability Theory ◽  
Convergence Time ◽  
Control Approach ◽  
Finite Time Stability

This paper concerns the problem of stabilization of uncertain fractional-order chaotic systems in finite time. On the basis of fractional Lyapunov stability theory, a robust finite-time fractional controller is introduced to control chaos of fractional-order chaotic systems in the presence of system uncertainties. The finite-time stability of the closed-loop system is analytically proved. An estimation of the convergence time is also given. Some numerical simulations are provided to illustrate the usefulness and applicability of the proposed robust finite-time control approach. It is worth noting that the proposed fractional control method is applicable for stabilizing a broad range of uncertain fractional-order nonlinear systems in a given finite time.

scholarly journals Finite-time generalized synchronization of nonidentical delayed chaotic systems

2016 ◽  
Vol 21 (3) ◽  
pp. 306-324 ◽  
Author(s):  
Haibo Bao ◽  
Jinde Cao
Keyword(s):  
Finite Time ◽  
Chaotic Systems ◽  
Sufficient Conditions ◽  
Convergence Time ◽  
Generalized Synchronization ◽  
Delayed Systems ◽  
Finite Time Stability ◽  
Control Techniques ◽  
Nonlinear Control Theory ◽  
Response Systems

This paper deals with the finite-time generalized synchronization (GS) problem of drive-response systems. The main purpose of this paper is to design suitable controllers to force the drive-response system realize GS in a finite time. Based on the finite-time stability theory and nonlinear control theory, sufficient conditions are derived that guarantee finite-time GS. This paper extends some basic results from generalized synchronization to delayed systems. Because finite-time GS means the optimality in convergence time and has better robustness, the results in this paper are important. Numerical examples are given to show the effectiveness of the proposed control techniques.

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