The infinite-scroll attractor and energy transition in chaotic circuit

Abstract

Nonlinear oscillators composed of multi-scroll chaotic attractor show much more complicate and rich chaotic dynamics and are often used for generating complex secure keys and carrying wave for secure communication or image encryption. Indeed, controllers designed as piecewise-linear functions are used to induce multi-scroll attractors in nonlinear circuits by generating a group of equilibrium points. In this paper, we present a feasible but practical scheme which can generate infinite-scroll attractor by replacing the nonlinear terms in the improved Chua circuit with a sine function. It is found that the number of multi-scroll attractor increases with the calculating period increasing as infinite equilibrium points could be induced for the sine function. Interestingly, the Hamilton energy of the circuits composed of multi-scroll attractor, defined by the Helmholtz’ s theorem, is decreased with the number increasing of multi-scroll attractor. This result indicates that power consumption of circuit devices could be decreased when multi-scroll attractor is stabilized. Furthermore, a scheme is presented to stabilize the multi-scroll attractor by applying negative type of coupling on the chaotic system.