Dynamics, Analysis and Implementation of a Multiscroll Memristor-Based Chaotic Circuit

Abstract

This article introduces a novel four-dimensional autonomous multiscroll chaotic circuit which is derived from the actual simplest memristor-based chaotic circuit. A fourth circuit element — another inductor — is introduced to generate the complex behavior observed. A systematic study of the chaotic behavior is performed with the help of some nonlinear tools such as Lyapunov exponents, phase portraits, and bifurcation diagrams. Multiple scroll attractors are observed in Matlab, Pspice environments and also experimentally. We also observe the phenomenon of antimonotonicity, periodic and chaotic bubbles, multiple periodic-doubling bifurcations, Hopf bifurcations, crises and the phenomenon of intermittency. The chaotic dynamics of this circuit is realized by laboratory experiments, Pspice simulations, numerical and analytical investigations. It is observed that the results from the three environments agree to a great extent. This topology is likely convenient to be used to intentionally generate chaos in memristor-based chaotic circuit applications, given the fact that multiscroll chaotic systems have found important applications as broadband signal generators, pseudorandom number generators for communication engineering and also in biometric authentication.

Design and Realization of a Hyperchaotic Memristive System for Communication System on FPGA

“…The Lyapunov exponents method is a mathematical analysis method that shows whether the time series of the system has chaotic components. In addition, this method shows the numerical expression of the sensitivity to initial conditions, one of the most important features of chaotic systems and the Lyapunov exponent is represented by L [34]. L1=0.31, L2=0.0097, L3=-0.0098 and L4=-30.21 are obtained when the parameters are fixed as specified (a=7, b=1, c=2.5, d=1, m0=-1.2, m1=1 and n=-6) and this system is started to run for initial conditions (0.1, 0, 0, 0).…”

Hopf bifurcation, offset boosting and remerging Feigenbaum trees in an autonomous chaotic system with exponential nonlinearity

“…Many studies have proven that nonlinear dissipative systems can be dissipative and thus support chaotic attractors [37][38][39]. In short, the volume contraction rate of a dynamical system can be studied by the divergence of its vector field; it is defined as:…”

Use of memristor-based chaotic circuits in AM-DCSK and FM-DCSK modulation

“…Many different models of memristor emulators and memristor based systems have been presented in the literature over the past few years [15][16][17][18]. Using these memristor emulators, various nonlinear memristor-based circuits have been proposed and their dynamic behavior have been studied [19][20][21][22][23][24]. One of the interesting issues recently arisen in nonlinear electronic systems is the implementation of memristor-based oscillators [25][26][27].…”