Extreme multistability: Attractor manipulation and robustness

TL;DR

This paper introduces a general coupling design that induces extreme multistability in coupled dynamical systems, enabling control over attractor states and demonstrating robustness to parameter mismatches.

Contribution

It proposes a novel coupling scheme that induces extreme multistability and partial synchronization, expanding the understanding and control of complex dynamical behaviors.

Findings

Coupling design induces extreme multistability in systems.

The phenomenon is robust to parameter mismatches.

The scheme allows control over attractor amplitudes.

Abstract

The coexistence of infinitely many attractors is called extreme multistability in dynamical systems. In coupled systems, this phenomenon is closely related to partial synchrony and characterized by the emergence of a conserved quantity. We propose a general design of coupling that leads to partial synchronization, which may be a partial complete synchronization or partial antisynchronization and even a mixed state of complete synchronization and antisynchronization in two coupled systems and, thereby reveal the emergence of extreme multistability. The proposed design of coupling has wider options and allows amplification or attenuation of the amplitude of the attractors whenever it is necessary. We demonstrate that this phenomenon is robust to parameter mismatch of the coupled oscillators.