Multistability and its dependence on the attractor volume

Abstract

Multistability is an important concept that refers to the coexistence of multiple solutions. Although significant studies reported the emergence of multistability, a few studies have been devoted to investigating its features. This paper is dedicated to addressing the volume dependence of multistability as its extensive feature using theoretical and numerical aspects. The results of the forward and backward dynamical analysis of the modulated laser system and the Duffing oscillator show that multistability takes place when the attractor volume becomes large enough to meet other solutions. On the other hand, when the attractor volume is small, the system solution has no chance to visit other attractors, and multistability cannot occur. Furthermore, our results suggest that the dissipation diagram, which is normalized to the attractor volume, can detect the multistability regions since it simultaneously includes information about the dissipation and attractor volumes.