Hyperchaos in a Modified Canonical Chua's Circuit

Abstract

In this paper, we present the hyperchaos dynamics of a modified canonical Chua's electrical circuit. This circuit, which is capable of realizing the behavior of every member of the Chua's family, consists of just five linear elements (resistors, inductors and capacitors), a negative conductor and a piecewise linear resistor. The route followed is a transition from regular behavior to chaos and then to hyperchaos through border-collision bifurcation, as the system parameter is varied. The hyperchaos dynamics, characterized by two positive Lyapunov exponents, is described by a set of four coupled first-order ordinary differential equations. This has been investigated extensively using laboratory experiments, Pspice simulation and numerical analysis.

Active Controller Design For Global Chaos Synchronization Of Hyperchaotic Bao And Hyperchaotic Xu Systems

“…For the numerical simulations, the fourth order Runge-Kutta method with initial timestep 6 10 h − = is used to solve the two systems of differential equations (24) and (25) …”

“…Thus, the hyperchaotic systems have more complex dynamical behaviour which can be used to improve the security of a chaotic communication system. Hence, the theoretical design and circuit realization of various hyperchaotic signals have become important research topics [23][24][25][26][27].…”

Scaling Synchronization of a 6D Hyperchaotic System

“…Hyperchaotic system is one of the critical issues in nonlinear science and attracted considerable attention due to it is theoretical and practical applications in lasers [28] , nonlinear circuits [27], and secure communication [32], and so on. Controlling these complex dynamics for engineering applications has emerged as a new and attractive field and has developed many profound theories and methodologies [1,15].…”

Some new less conservative criteria for impulsive synchronization of a hyperchaotic Lorenz system based on small impulsive signals

“…Hence, the generation, control, synchronization and application of hyperchaos have recently become a hot topic for research in this regard [1][2][3][4][5][6]. A large variety of hyperchaotic systems have been presented over the past few decades.…”

“…A large variety of hyperchaotic systems have been presented over the past few decades. For example, the hyperchaotic Chua's circuit [1] and Rossler system [2] are two representative hyperchaotic systems. Recently, several new hyperchaotic systems have been proposed.…”