Synchronisation of the hyperchaotic complex Lorenz system in a finite time

2016 ◽  
Vol 25 (2) ◽  
pp. 138 ◽  
Author(s):  
Homayoon Arabyani ◽  
Hassan Saberi Nik
Keyword(s):  
Finite Time ◽  
Lorenz System ◽  
Complex Lorenz System

The characteristics and self-time-delay synchronization of two-time-delay complex Lorenz system

2019 ◽  
Vol 356 (1) ◽  
pp. 334-350 ◽  
Author(s):  
Baojiang Sun ◽  
Min Li ◽  
Fangfang Zhang ◽  
Hui Wang ◽  
Jian Liu
Keyword(s):  
Time Delay ◽  
Lorenz System ◽  
Complex Lorenz System

Analysis of a Nonlinear System with a Random Parameter

2014 ◽  
Vol 721 ◽  
pp. 366-369
Author(s):  
Hong Gang Dang ◽  
Xiao Ya Yang ◽  
Wan Sheng He
Keyword(s):  
Nonlinear System ◽  
Fractional Order ◽  
Approximation Method ◽  
Lorenz System ◽  
Laguerre Polynomial ◽  
Random Parameter ◽  
Order System ◽  
Order Complex ◽  
Ensemble Mean ◽  
Complex Lorenz System

In this paper, a nonlinear system with random parameter, which is called stochastic fractional-order complex Lorenz system, is investigated. The Laguerre polynomial approximation method is used to study the system. Then, the stochastic fractional-order system is reduced into the equivalent deterministic one with Laguerre approximation. The ensemble mean and sample responses of the stochastic system can be obtained.

scholarly journals A New Fractional-Order Chaotic Complex System and Its Antisynchronization

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Cuimei Jiang ◽  
Shutang Liu ◽  
Chao Luo
Keyword(s):  
Complex System ◽  
Fractional Order ◽  
Lorenz System ◽  
Chaotic Behavior ◽  
Phase Portraits ◽  
Chaotic Attractors ◽  
Fractional Order Systems ◽  
Chaotic Complex System ◽  
The Stability ◽  
Complex Lorenz System

We propose a new fractional-order chaotic complex system and study its dynamical properties including symmetry, equilibria and their stability, and chaotic attractors. Chaotic behavior is verified with phase portraits, bifurcation diagrams, the histories, and the largest Lyapunov exponents. And we find that chaos exists in this system with orders less than 5 by numerical simulation. Additionally, antisynchronization of different fractional-order chaotic complex systems is considered based on the stability theory of fractional-order systems. This new system and the fractional-order complex Lorenz system can achieve antisynchronization. Corresponding numerical simulations show the effectiveness and feasibility of the scheme.

scholarly journals Synchronization of Lorenz System Based on Fast Stabilization Sliding Mode Control

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Xu Guowei ◽  
Wan Zhenkai ◽  
Li Chunqing
Keyword(s):  
Sliding Mode Control ◽  
Finite Time ◽  
Lorenz System ◽  
Sliding Mode ◽  
External Perturbation ◽  
Lyapunov Theory ◽  
Continuous Control ◽  
Integral Sliding Mode ◽  
Control Approach ◽  
Mode Control

A sliding mode control approach is achieved for Lorenz system based on optimal finite time convergent and integral sliding mode surface. The system perturbation is divided into two parts: the unmatched and the matched parts. Firstly, we design a discontinuous control for the unmatched part which will not be amplified. Secondly, we design a continuous control, that is, the ideal control to stabilize the Lorenz system error states in finite time stabilization. Then the controller based on integral sliding mode is constructed to ensure the robustness. The proposed method is proven to guarantee the stability and the robustness using the Lyapunov theory in the system uncertainties and external perturbation. Finally, the numerical simulations demonstrate that the proposed controller is effective and robust with respect to the perturbation.

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