Controlling multistability by discontinuous dissipative coupling

TL;DR

This paper investigates how discontinuous dissipative coupling via impacts influences multistable oscillatory systems, demonstrating control over the number of stable solutions through parameter adjustments.

Contribution

It introduces a novel method of controlling multistability in coupled oscillators using impact-based discontinuous coupling, with demonstrated robustness and broad applicability.

Findings

Discontinuous coupling reduces the number of stable solutions.

Proper parameter tuning can control system multistability.

Impact dynamics lead to convergence on non-impacting attractors.

Abstract

In this paper we present an influence of discontinuous coupling on the dynamics of multistable systems. Our model consists of two periodically forced oscillators that can interact via soft impacts. The controlling parameters are the distance between the oscillators and the difference in the phase of the harmonic excitation. When the distance is large two systems do not collide and a number of different possible solutions can be observed in both of them. When decreasing of the distance, one can observe some transient impacts and then the systems settle down on non-impacting attractor. It is shown that with the properly chosen distance and difference in the phase of the harmonic excitation, the number of possible solutions of the coupled systems can be reduced. The proposed method is robust and applicable in many different systems.