scholarly journals A Memristor-Based Complex Lorenz System and Its Modified Projective Synchronization

Entropy ◽  
2015 ◽  
Vol 17 (12) ◽  
pp. 7628-7644 ◽  
Author(s):  
Shibing Wang ◽  
Xingyuan Wang ◽  
Yufei Zhou
Keyword(s):  
Lorenz System ◽  
Projective Synchronization ◽  
Modified Projective Synchronization ◽  
Complex Lorenz System

scholarly journals Hybrid Synchronization of Uncertain Generalized Lorenz System by Adaptive Control

2018 ◽  
Vol 2018 ◽  
pp. 1-5 ◽  
Author(s):  
Xinlian Zhou ◽  
Yuhua Xu
Keyword(s):  
Adaptive Control ◽  
Lorenz System ◽  
Projective Synchronization ◽  
Reduced Order ◽  
Parameter Update Law ◽  
Generalized Lorenz System ◽  
Stability Point ◽  
Modified Projective Synchronization ◽  
Hybrid Synchronization ◽  
The Stability

This paper investigates hybrid synchronization of the uncertain generalized Lorenz system. Several useful criteria are given for synchronization of two generalized Lorenz systems, and the adaptive control law and the parameter update law are used. In comparison with those of existing synchronization methods, hybrid synchronization includes full-order synchronization, reduced-order synchronization, and modified projective synchronization. What is more, control of the stability point, complete synchronization, and antisynchronization can coexist in the same system. Numerical simulations show the effectiveness of this method in a class of chaotic systems.

Hybrid Projective Synchronization of Fractional-Order Chaotic Complex Nonlinear Systems With Time Delays

2015 ◽  
Vol 11 (3) ◽  
Author(s):  
G. Velmurugan ◽  
R. Rakkiyappan
Keyword(s):  
Nonlinear Systems ◽  
Fractional Order ◽  
Time Delays ◽  
Lorenz System ◽  
Projective Synchronization ◽  
Nonlinear Controller ◽  
Scaling Factors ◽  
Hybrid Projective Synchronization ◽  
Complex Nonlinear Systems ◽  
Complex Lorenz System

Time delays are frequently appearing in many real-life phenomena and the presence of time delays in chaotic systems enriches its complexities. The analysis of fractional-order chaotic real nonlinear systems with time delays has a plenty of interesting results but the research on fractional-order chaotic complex nonlinear systems with time delays is in the primary stage. This paper studies the problem of hybrid projective synchronization (HPS) of fractional-order chaotic complex nonlinear systems with time delays. HPS is one of the extensions of projective synchronization, in which different state vectors can be synchronized up to different scaling factors. Based on Laplace transformation and the stability theory of linear fractional-order systems, a suitable nonlinear controller is designed to achieve synchronization between the master and slave fractional-order chaotic complex nonlinear systems with time delays in the sense of HPS with different scaling factors. Finally, the HPS between fractional-order delayed complex Lorenz system and fractional-order delayed complex Chen system and that of fractional-order delayed complex Lorenz system and fractional-order delayed complex Lu system are taken into account to demonstrate the effectiveness and feasibility of the proposed HPS techniques in the numerical example section.

Adaptive Hybrid Function Projective Synchronization of General Chaotic Complex Systems With Different Orders

2015 ◽  
Vol 10 (2) ◽  
Author(s):  
Ping Liu
Keyword(s):  
Nonlinear Systems ◽  
Complex Systems ◽  
Lorenz System ◽  
Mathematical Expression ◽  
Projective Synchronization ◽  
Unknown Parameters ◽  
Chen System ◽  
Function Projective Synchronization ◽  
Hybrid Function ◽  
Complex Lorenz System

A lot of progress has been made in the research of hybrid function projective synchronization (HFPS) for chaotic real nonlinear systems, while the HFPS of two different chaotic complex nonlinear systems with nonidentical dimensions is seldom reported in the literatures. So this paper discusses the HFPS of general chaotic complex system described by a unified mathematical expression with different dimensions and fully unknown parameters. Based on the Lyapunov stability theory, the adaptive controller is designed to synchronize two general uncertain chaotic complex systems with different orders in the sense of HFPS and the parameter update laws for estimating unknown parameters of chaotic complex systems are also given. Moreover, the control coefficients can be automatically adapted to updated laws. Finally, the HFPS between hyperchaotic complex Lorenz system and complex Chen system and that between chaotic complex Lorenz system and hyperchaotic complex Lü are taken as two examples to demonstrate the effectiveness and feasibility of the proposed HFPS scheme.

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.

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