Homogenous Multistability in Memristive System

Abstract

Many dynamical systems may have special parameters to control the amplitude sometimes concomitantly with frequency or offset. In this chapter, we select a chaotic system with amplitude-frequency parameter, which controls the scale and speed of the oscillation without changing its basic property of chaos. By introducing a memristor into the feedback for amplitude/frequency control, a special regime of homogenous multistability shows up in memristive system where the initial condition of the internal variable only determines the amplitude (here combined with frequency) of the variables without changing the essential oscillation of chaos. This phenomenon can exist in other systems with scale parameter. Unlike other regular multistability, the coexisting attractors share the same shape of phase trajectory except with different scales. Following this routine, a new pattern of homogenous multistability is also demonstrated where the stable oscillation stands in phase space with different offset in the dimension of x without changing the fundamental oscillation. To our best knowledge, it is reported firstly on homogenous multistability in memristive system systematically.