Generation of Multistability through Unstable Systems

Abstract

In this work, we propose an approach to generate multistability based on a class of unstable systems that have all their roots in the right complex half-plane. Multistability is the coexistence of multiple stable states for a set of system parameters. The approach is realized by using linear third order differential equations that consists of two parameters. The first bifurcation parameter transforms the unstable system with all its roots in the right complex half-plane into an unstable system with one root in the left complex half-plane and two roots remaining in the right complex half-plane. With this first transformation, the system is capable of generating attractors by means of a piecewise linear function and the system presents monostability. We then use the another bifurcation parameter to switch from a monostable multiscroll attractor to several multistable states showing a single-scroll attractor.