New 3d-Scroll Attractors in Hyperchaotic Chua's Circuits Forming a Ring

Abstract

This paper presents an approach for generating new hyperchaotic attractors in a ring of Chua's circuits. By taking a closed chain of three circuits and exploiting sine functions as nonlinearities, the proposed technique enables 3D-scroll attractors to be generated. In particular, the paper shows that 3D-scroll dynamics can be designed by modifying six parameters related to the circuit nonlinearities.

Analysis and Implementation of a New Switching Memristor Scroll Hyperchaotic System and Application in Secure Communication

“…It is clear that S 0 is the first type saddle point since the real eigenvalue is positive [25,26]. It is noticed that the scrolls are generated only around the equilibria of saddle points of index 2 [25,26].…”

“…The Equilibria S 1 and S 2 could have eigenvalues λ 1 = −5 9483 + 13 6659i, λ 2 = −5 9483 − 13 6659i, λ 3 = 0 4983 + 6 9549i, and λ 4 = 0 4983 − 6 9549i, which are called saddle points of index 2 since the two complex conjugate eigenvalues have positive real parts [25,26]. It is clear that S 0 is the first type saddle point since the real eigenvalue is positive [25,26].…”

Circuit Simulation of the Modified Lorenz System

“…As well known, since Lorenz discovered a chaotic system in 1963 [1], the investigation of chaotic behavior in nonlinear systems has attracted great attention. Besides the Lorenz system, there are Rössler system [2], Chua's circuit [3], Chen system [4]. In 2002, Lü and Chen propose an intermediate chaotic system, called the Lü system system [5], which provides the transition between the Lorenz system and the Chen system.…”

Multiscroll in Coupled Double Scroll Type Oscillators

“…The trajectory switches irregularly from one to the other symmetric locations but always repelled by the third saddle focus origin. Multiscroll attractors have a larger number of scrolls (n>2, n is the number of scroll) and mostly been implemented [Kapitaniak et al, 1990;Kapitaniak et al, 1994;Suykens et al, 1993;Arena et al, 1996;Tang et al, 2001;Yalcin et al, 2000;Yalcin et al, 2001;Lü et al, 2003;Ozoguz et al, 2002;Cafagna et al, 2003;Lü et al, 2004;Lü et al, 2004a;Yu et al, 2006; by introducing additional saddle foci in terms of added breakpoints in the model system. Multiscroll has been reported in unidirectionally or diffusively coupled self-oscillating Chua circuits [Kapitaniak and Chua, 1994] and in arrays of 1-D cellular neural networks (CNN) [Suykens and Vandewalle, 1993], where the birth of a double-double scroll attractor is found in intermittent bursts from 3D manifold to higher dimensions for weaker coupling.…”

“…However, in such attempts too, for the generation of multiscroll, additional break point was necessitated in the piecewise linear function of the Chua circuit. The electronic implementation of multiscroll is done with different circuit schemes by adding multiple breakpoints in the piecewise linear function of the system [Kapitaniak et al, 1994;Suykens et al, 1993;Arena et al, 1996;Suykens et al, 1997;Yalcin et al, 2000;Yalcin et al, 2001, Cafagna et al, 2003], by using a sine function [Tang et al, 2001] or by adding saturated function series [Lü et al, 2004]. Hysteresis [Lü et al, 2004a] is also used sometimes for the generation of n-scroll chaos.…”