An approach toward higher dimensional hysteresis chaos generators

Abstract

Abstrnct -This paper discusses an approach toward higher dimensional autonomous chaotic circuits. We especially consider a particular class of circuits which includes only one nonlinear element, a three segments piecewise-linear resistor, and one small inductor La serially connected with it. The contents are divided into two parts. Part 1 gives a simple fourdimensional example that realizes hyperchaos. For the case where La is shorted, the circuit equation can be simplified into a constrained system and a two-dimensional Poincare map can be rigorously derived. This mapping and its Lyapunov exponents verify laboratory measurements of hyperchaos and related phenomena. Part 2 gives a rigorous approach to the singular perturbation theory of a N-dimensional circuit family which includes the example in Section I. We derive a canonical form equation which describes any circuit in this family. This equation can be simplified into a constrained system and a (N -2)-dimensional Poincare map can be derived. The main theorem indicates that this mapping explains the observable solutions of the canonical form very well.PART 1 A HYPERCHAOSGENERATOR

Harmonic Balance Analysis of the Generalized Chua's Circuit

“…The comparable generalizations have been given in [Kataoka & Saito, 1999;Kocarev et al, 1993;Madan, 1993;Saito, 1990;Wu & Chua, 1996], however, in these papers either the models are hard to be realized or the dimension of the proposed models are higher than that of the original Chua's circuit.…”

Design and Analysis of Multiscroll Chaotic Attractors From Saturated Function Series

“…The controlled system is (24) with defined by (5), and are positive constants. In addition to (14), (15), (18), and (19), define (25) and (26) Assume that (13) and (20) hold and (27) Then, (24) has equilibrium points, given by (28) Note that all equilibria can be classified into eight different sets:…”

“…In particular, a 2-D Poincaré return map [18], [26] is rigorously derived for verifying the chaotic behaviors of the double-scroll system (11).…”

Families of Scroll Grid Attractors

“…As a result, it is possible to increase the number of scrolls into all state variable directions. In the literature, a quad screw attractor [Kataoka & Saito, 2000] from a 4D chaotic oscillator with hysteresis [Saito, 1990] is comparable with a 2 × 2-scroll grid attractor, which is a member of the 2D-grid scroll attractor family. However, it should be noted that the system presented here is simpler than the other one.…”