Analysis of a Variable-Order Multi-scroll Chaotic System with Different Memory Lengths

Abstract

This work presents a numerical analysis of the dynamical behavior of a multi-scroll chaotic system using variable-order calculus. In this scenario, we introduce the concept of variable-order from two approaches denominated herein as short-memory and full-memory, respectively. For the first one, the basic idea is to study the chaotic dynamics when the fractional-order changes abruptly like step-function with respect to time. The second approach is related to a smoother variation between the preceding order and the new fractional-order. To demonstrate the implications of using variable-order with distinct memory contributions, we show several numerical simulations of a multi-scroll chaotic system that contains a piecewise linear function. Numerical results are consistent with the underlying theory demonstrating the usefulness of the proposed study.