Mechanism of multistability in chaotic maps

Abstract

This research aims to investigate the mechanisms of multistability in chaotic maps. The study commences by examining the fundamental principles governing the development of homogeneous multistability using a basic one-dimensional chain-climbing map. Findings suggest that the phase space can be segmented into distinct uniform mediums where particles exhibit consistent movement. As critical parameter values are reached, channels emerge between these mediums, resulting in deterministic chaotic diffusion. Additionally, the study delves into the topic of introducing heterogeneous factors on the formation of heterogeneous multistability in the one-dimensional map. A thorough examination of phenomena such as multistate intermittency highlights the intimate connection between specific phase transition occurrences and channel formation. Finally, by analyzing two instances—a memristive chaotic map and a hyperchaotic map—the underlying factors contributing to the emergence of multistability are scrutinized. This study offers an alternative perspective for verifying the fundamental principles of homogenous and heterogeneous multistability in complex high-dimensional chaotic maps.