Coexisting hollow chaotic attractors within a steep parameter interval

Abstract

By transforming the past states of a variable to another variable, and returning the evolvement along with various functions of self-feedback, a unique gallery of chaotic maps with coexisting hollow attractors is proposed. Strikingly, these peculiar attractors stand on steep parameter intervals, some of which could only happen when the parameter accurately approaches the integer 1 instead of 1. Some maps also have direct amplitude controllers, which regulate the dynamics together with the initial condition leaving unpredicted complexity. The nested hollow attractors are arranged in phase space with great distribution diversity in the form of homogeneous and heterogeneous multistability. CH32-based digital circuit experiments show agreement with numerical simulation and theoretical prediction. Furthermore, the application in secure optical communication is explored accordingly proving higher performance in the steep parameter interval.