Chua’s Equation With Cubic Nonlinearity

Abstract

In this tutorial paper we present one of the simplest autonomous differential equations capable of generating chaotic behavior. Some of the fundamental routes to chaos and bifurcation phenomena are demonstrated with examples. A brief discussion of equilibrium points and their stability is given. For the convenience of the reader, a short computer program written in QuickBASIC is included to give the reader a possibility of quick hands-on experience with the generation of chaotic phenomena without using sophisticated numerical simulators. All the necessary parameter values and initial conditions are provided in a tabular form. Eigenvalue diagrams showing regions with particular eigenvalue patterns are given.

Mixed outer synchronization of coupled complex networks with time-varying coupling delay

“…In fact, it is easy to check that some general chaotic systems such as original Chua's circuit, 40 modified Chua's circuit, [41][42][43][44] fourth-order Chua's circuit, 45,46 Chua's circuit family, 47 and Chua's oscillator, 48 can be decomposed into such a form. Thus, network (1) is rewritten as…”

Chaos Synchronization: A Lagrange Programming Network Approach

“…We apply the synchronization schemes by assuming the existence of a potential function for each of the subsystems, eventually in a more generalized sense than characterized by (17). Strictly speaking, in fact smooth versions to Chua's circuit and n-scroll circuits [Huang et al, 1996;Ponomarenko & Matrosov, 1996] should be considered. However, simulation results suggest that the piecewise-linear nature of the circuits does not pose a problem in the examples that have been investigated.…”

“…In many cases the Lagrange programming network shows an improved performance compared to standard schemes that correspond to soft constraining. Theoretically speaking smooth versions to Chua's circuit and n-scroll circuits [Huang et al, 1996;Ponomarenko & Matrosov, 1996] should be considered. However, simulation results suggest that the piecewise-linear nature of the circuits does not pose a problem for the investigated examples.…”

Experimental confirmation of 3- and 5-scroll attractors from a generalized Chua's circuit

“…Among the generalizations that have been proposed in literature [8], [10]- [12], [21], Suykens and Vandewalle [13], [14] introduced a family of n-double scroll attractors, where n is a natural number. An experimental confirmation of 2-double scrolls has been given by Arena et al in [1], [2].…”