Narrow Results

In this tutorial paper, we present some interesting phenomena from Chua's equation with a cubic nonlinearity as well as that with a piecewise-linear characteristic, where a cubic polynomial approximates the original three-segment piecewise-linear function. A gallery of attractors and bifurcation diagrams obtained by numerical simulations are presented. We hope this will motivate researchers to study the smooth version of this extremely simple yet versatile equation with more than 20 attractors.

In this paper, smooth Chua's equation is generalized to a higher order system from a special viewpoint of interconnected systems. Simple conditions for Lagrange stability are established. And a detailed Lagrange stable region analysis is given for the canonical Chua's oscillator. In addition, a new nonlinearly coupled Chua's circuit that appeared in the recent literature is also discussed and a Lagrange stability condition is presented. Several examples are presented to illustrate the results.

In this paper, chaos in the smooth Chua's equation is revisited. To confirm the chaotic behavior in the smooth Chua's equation demonstrated in numerical studies, we resort to Poincaré section and Poincaré map technique and present a computer assisted verification of existence of horseshoe chaos by virtue of topological horseshoes theory.