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

Abstract

Abstract: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.

A Memristor-Based Hyperchaotic Complex Lü System and Its Adaptive Complex Generalized Synchronization

“…As introduced in [23,44,45], transient phenomena can appear in some memristor-based nonlinear systems, which need much longer computational time to achieve the steady states of the system. Hence, we use ode45 solver of Matlab®R2013a to simulate the system for plotting bifurcation diagram and calculating Lyapunov exponents with computational time interval 0-20,000 s and 0-100,000 s separately.…”

Meromorphic Non-Integrability of Several 3D Dynamical Systems

“…Since (3) is a linear differential equation, we can consider the differential Galois group corresponding to (3). Generally speaking, the differential Galois group G of (3) is a matrix subgroup of GL(n − 1, C) acting on the fundamental solutions of (3) such that it dose not change polynomial and differential relations between them.…”

“…To deal with the issue, one should show that the system has positive Lyapunov exponents or metric entropy, heteroclinic connections, and so on (see for instance [1][2][3]). There is much literature on the complex behavior and non-integrability of dynamical systems.…”

Circuit Implementation, Synchronization of Multistability, and Image Encryption of a Four-Wing Memristive Chaotic System

“…Some researchers added the memristor model to Chua's circuit [13], and others combined the Lorenz system with memristors [14]. In recent years, a lot of attention has been paid to the research on the memristive chaotic circuits applied to synchronization, and the synchronization scheme of memristive chaos based on Lorenz system has been developed initially [15,16]. Master system and slave system can achieve chaotic synchronization under controlled constraints, and it has been widely used in secure communication and other fields [17,18].…”