Global finite-time synchronization of a class of the non-autonomous chaotic systems

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.

Download Full-text

A generalized finite-time analytical approach for the synchronization of chaotic and hyperchaotic systems

Multidiscipline Modeling in Materials and Structures ◽

10.1108/mmms-06-2020-0131 ◽

2020 ◽

Vol ahead-of-print (ahead-of-print) ◽

Author(s):

Muhammad Haris ◽

Muhammad Shafiq ◽

Adyda Ibrahim ◽

Masnita Misiran

Keyword(s):

Finite Time ◽

Chaotic Systems ◽

Closed Loop ◽

Time Synchronization ◽

Linear Part ◽

Content Type ◽

Nonlinear Part ◽

Analytical Stability ◽

Chaotic Signals ◽

The Stability

PurposeThe purpose of this paper is to develop some interesting results in the field of chaotic synchronization with a new finite-time controller to reduce the time of convergence.Design/methodology/approachThis article proposes a finite-time controller for the synchronization of hyper(chaotic) systems in a given time. The chaotic systems are perturbed by the model uncertainties and external disturbances. The designed controller achieves finite-time synchronization convergence to the steady-state error without oscillation and elimination of the nonlinear terms from the closed-loop system. The finite-time synchronization convergence reduces the hacking duration and recovers the embedded message in chaotic signals within a given preassigned limited time. The free oscillation convergence keeps the energy consumption low and alleviates failure chances of the actuator. The proposed finite-time controller is a combination of linear and nonlinear parts. The linear part keeps the stability of the closed-loop, the nonlinear part increases the rate of convergence to the origin. A generalized form of analytical stability proof is derived for the synchronization of chaotic and hyper-chaotic systems. The simulation results provide the validation of the accomplish synchronization for the Lu chaotic and hyper-chaotic systems.FindingsThe designed controller not only reduces the time of convergence without oscillation of the trajectories which can run the system for a given time domain.Originality/valueThis work is originally written by the author.

Download Full-text

Finite time synchronization of chaotic systems with unmatched uncertainties

30th Annual Conference of IEEE Industrial Electronics Society, 2004. IECON 2004 ◽

10.1109/iecon.2004.1432272 ◽

2005 ◽

Cited By ~ 15

Author(s):

Yong Feng ◽

Lixia Sun ◽

Xinghuo Yu

Keyword(s):

Finite Time ◽

Chaotic Systems ◽

Time Synchronization ◽

Unmatched Uncertainties

Download Full-text

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

Mathematical Problems in Engineering ◽

10.1155/2016/7693547 ◽

2016 ◽

Vol 2016 ◽

pp. 1-14 ◽

Cited By ~ 6

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.

Download Full-text