Finite-Time Synchronization for High-Dimensional Chaotic Systems and Its Application to Secure Communication

2016 ◽  
Vol 11 (5) ◽  
Author(s):  
Yongjian Liu ◽  
Lijie Li ◽  
Yu Feng
Keyword(s):  
Finite Time ◽  
Secure Communication ◽  
Chaotic Systems ◽  
Time Synchronization ◽  
Control Technique ◽  
High Dimensional ◽  
Time Stability ◽  
Finite Time Stability ◽  
Information Signal ◽  
Hyperchaotic Systems

The finite-time synchronization for the high-dimensional chaotic system is studied. A method is derived from the finite-time stability theory and adaptive control technique. To show the wider applicability of our method, an illustration is given using four-dimensional (4D) hyperchaotic systems. Numerical simulations are also used to verify the effectiveness of the technique. Then, the synchronization is applied to secure communication through chaos masking. Simulation results show that the two high-dimensional chaotic systems can realize monotonous synchronization, and the information signal, which is masked, can be recovered undistortedly.

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 Adaptive Modified Function Projective Multi–Lag Generalized Compound Synchronization for Multiple Uncertain Chaotic Systems

2018 ◽  
Vol 28 (4) ◽  
pp. 613-624
Author(s):  
Qiaoping Li ◽  
Sanyang Liu ◽  
Yonggang Chen
Keyword(s):  
Adaptive Control ◽  
Finite Time ◽  
Chaotic Systems ◽  
Time Synchronization ◽  
Control Technique ◽  
Unknown Parameters ◽  
Theoretical Derivation ◽  
Finite Time Stability ◽  
Compound Synchronization ◽  
Different Chaotic Systems

Abstract In this paper, for multiple different chaotic systems with fully unknown parameters, a novel synchronization scheme called ‘modified function projective multi-lag generalized compound synchronization’ is put forward. As an advantage of the new method, not only the addition and subtraction, but also the multiplication of multiple chaotic systems are taken into consideration. This makes the signal hidden channels more abundant and the signal hidden methods more flexible. By virtue of finite-time stability theory and an adaptive control technique, a finite-time adaptive control scheme is established to realize the finite-time synchronization and to properly evaluate the unknown parameters. A detailed theoretical derivation and a specific numerical simulation demonstrate the feasibility and validity of the advanced scheme.

scholarly journals Finite-Time Combination-Combination Synchronization for Hyperchaotic Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Huini Lin ◽  
Jianping Cai ◽  
Jincheng Wang
Keyword(s):  
Finite Time ◽  
Time Synchronization ◽  
Control Method ◽  
Control Technique ◽  
Finite Time Stability ◽  
Combination Synchronization ◽  
Response Systems ◽  
Nonlinear Control Method ◽  
Drive Systems ◽  
Hyperchaotic Systems

A new type of finite-time synchronization with two drive systems and two response systems is presented. Based on the finite-time stability theory, step-by-step control and nonlinear control method, a suitable controller is designed to achieve finite-time combination-combination synchronization among four hyperchaotic systems. Numerical simulations are shown to verify the feasibility and effectiveness of the proposed control technique.

Finite-time synchronization for fuzzy inertial cellular neural networks with time-varying delays via integral inequality

2021 ◽  
pp. 1-14
Author(s):  
Zhenjie Wang ◽  
Wenxia Cui ◽  
Wenbin Jin
Keyword(s):  
Neural Networks ◽  
Integral Inequality ◽  
Finite Time ◽  
Time Synchronization ◽  
Cellular Neural Networks ◽  
Time Varying ◽  
Time Stability ◽  
Finite Time Stability ◽  
Synchronization Problem ◽  
Inequality Techniques

This paper mainly considers the finite-time synchronization problem of fuzzy inertial cellular neural networks (FICNNs) with time-varying delays. By constructing the suitable Lyapunov functional, and using integral inequality techniques, several sufficient criteria have been proposed to ensure the finite-time synchronization for the addressed (FICNNs). Without applying the known finite-time stability theorem, which is widely used to solve the finite-time synchronization problems for (FICNNs). In this paper, the proposed method is relatively convenient to solve finite-time synchronization problem of the addressed system, this paper extends the research works on the finite-time synchronization of (FICNNs). Finally, numerical simulations illustrated verify the effectiveness of the proposed results.

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.

scholarly journals Finite-Time Synchronization of Complex Dynamical Networks with Time-Varying Delays and Nonidentical Nodes

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
Ahmadjan Muhammadhaji ◽  
Abdujelil Abdurahman ◽  
Haijun Jiang
Keyword(s):  
Complex Networks ◽  
Finite Time ◽  
Time Synchronization ◽  
Sufficient Conditions ◽  
Time Stability ◽  
Finite Time Stability ◽  
Uniformly Smooth ◽  
Nonidentical Nodes ◽  
Smooth State ◽  
Synchronization Performance

In this paper, we investigated the finite-time synchronization (FTS) problem for a class of time-delayed complex networks with nonidentical nodes onto any uniformly smooth state. By employing the finite-time stability theorem and designing two types of novel controllers, we obtained some simple sufficient conditions for the FTS of addressed complex networks. Furthermore, we also analyzed the effects of control variables on synchronization performance. Finally, we showed the effectiveness and feasibility of our methods by giving two numerical examples.

scholarly journals Finite-Time Synchronization of Chaotic Systems with Different Dimension and Secure Communication

2016 ◽  
Vol 2016 ◽  
pp. 1-14 ◽  
Author(s):  
Shouquan Pang ◽  
Yu Feng ◽  
Yongjian Liu
Keyword(s):  
Finite Time ◽  
Secure Communication ◽  
Chaotic Systems ◽  
Time Synchronization ◽  
Secure Communications ◽  
Hyperchaotic System ◽  
Uncertain Parameters ◽  
Three Dimension ◽  
Electronic Circuits ◽  
Lorenz Chaotic System

Finite-time synchronization of chaotic systems with different dimension and secure communication is investigated. It is rigorously proven that global finite-time synchronization can be achieved between three-dimension Lorenz chaotic system and four-dimension Lorenz hyperchaotic system which have certain parameters or uncertain parameters. The electronic circuits of finite-time synchronization using Multisim 12 are designed to verify our conclusion. And the application to the secure communications is also analyzed and discussed.

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.

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