A Memristor-Based Complex Lorenz System and Its Modified Projective Synchronization
The aim of this paper is to introduce and investigate a novel complex Lorenz system with a flux-controlled memristor, and to realize its synchronization. The system has an infinite number of stable and unstable equilibrium points, and can generate abundant dynamical behaviors with different paramete...
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doaj-d4d0036091574adebfc08fbe0f8d21352020-11-24T23:15:58ZengMDPI AGEntropy1099-43002015-11-0117117628764410.3390/e17117628e17117628A Memristor-Based Complex Lorenz System and Its Modified Projective SynchronizationShibing Wang0Xingyuan Wang1Yufei Zhou2Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian 116024, ChinaFaculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian 116024, ChinaCollege of Electrical Engineering and Automation, Anhui University, Hefei 230601, ChinaThe aim of this paper is to introduce and investigate a novel complex Lorenz system with a flux-controlled memristor, and to realize its synchronization. The system has an infinite number of stable and unstable equilibrium points, and can generate abundant dynamical behaviors with different parameters and initial conditions, such as limit cycle, torus, chaos, transient phenomena, etc., which are explored by means of time-domain waveforms, phase portraits, bifurcation diagrams, and Lyapunov exponents. Furthermore, an active controller is designed to achieve modified projective synchronization (MPS) of this system based on Lyapunov stability theory. The corresponding numerical simulations agree well with the theoretical analysis, and demonstrate that the response system is asymptotically synchronized with the drive system within a short time.http://www.mdpi.com/1099-4300/17/11/7628memristor-basedcomplex Lorenz systemnonlinear dynamicsmodified projective synchronization |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Shibing Wang Xingyuan Wang Yufei Zhou |
spellingShingle |
Shibing Wang Xingyuan Wang Yufei Zhou A Memristor-Based Complex Lorenz System and Its Modified Projective Synchronization Entropy memristor-based complex Lorenz system nonlinear dynamics modified projective synchronization |
author_facet |
Shibing Wang Xingyuan Wang Yufei Zhou |
author_sort |
Shibing Wang |
title |
A Memristor-Based Complex Lorenz System and Its Modified Projective Synchronization |
title_short |
A Memristor-Based Complex Lorenz System and Its Modified Projective Synchronization |
title_full |
A Memristor-Based Complex Lorenz System and Its Modified Projective Synchronization |
title_fullStr |
A Memristor-Based Complex Lorenz System and Its Modified Projective Synchronization |
title_full_unstemmed |
A Memristor-Based Complex Lorenz System and Its Modified Projective Synchronization |
title_sort |
memristor-based complex lorenz system and its modified projective synchronization |
publisher |
MDPI AG |
series |
Entropy |
issn |
1099-4300 |
publishDate |
2015-11-01 |
description |
The aim of this paper is to introduce and investigate a novel complex Lorenz system with a flux-controlled memristor, and to realize its synchronization. The system has an infinite number of stable and unstable equilibrium points, and can generate abundant dynamical behaviors with different parameters and initial conditions, such as limit cycle, torus, chaos, transient phenomena, etc., which are explored by means of time-domain waveforms, phase portraits, bifurcation diagrams, and Lyapunov exponents. Furthermore, an active controller is designed to achieve modified projective synchronization (MPS) of this system based on Lyapunov stability theory. The corresponding numerical simulations agree well with the theoretical analysis, and demonstrate that the response system is asymptotically synchronized with the drive system within a short time. |
topic |
memristor-based complex Lorenz system nonlinear dynamics modified projective synchronization |
url |
http://www.mdpi.com/1099-4300/17/11/7628 |
work_keys_str_mv |
AT shibingwang amemristorbasedcomplexlorenzsystemanditsmodifiedprojectivesynchronization AT xingyuanwang amemristorbasedcomplexlorenzsystemanditsmodifiedprojectivesynchronization AT yufeizhou amemristorbasedcomplexlorenzsystemanditsmodifiedprojectivesynchronization AT shibingwang memristorbasedcomplexlorenzsystemanditsmodifiedprojectivesynchronization AT xingyuanwang memristorbasedcomplexlorenzsystemanditsmodifiedprojectivesynchronization AT yufeizhou memristorbasedcomplexlorenzsystemanditsmodifiedprojectivesynchronization |
_version_ |
1725588676707090432 |