Front propagation in lattices with on-site bistable non-degenerate potential: multiplicity, bifurcations and route to chaos

TL;DR

This paper explores the complex dynamics of front propagation in lattices with bistable on-site potentials, revealing multiple bifurcation scenarios and routes to chaos through a novel implicit map formulation.

Contribution

It introduces a new implicit map approach to analyze front dynamics, uncovering multistability, bifurcations, and chaotic behavior in coupled oscillator lattices with non-degenerate potentials.

Findings

Stable fixed points correspond to travelling waves.

Loss of stability leads to bifurcations and complex dynamics.

Multiple types of propagating solutions, including chaotic regimes.

Abstract

Propagation of transition fronts in models of coupled oscillators with non-degenerate on-site potential is usually considered in terms of travelling waves. We show that the system dynamics can be reformulated as an implicit map structure, and the travelling waves correspond to stable fixed points. Therefore, the loss of stability of such waves should follow well-known generic bifurcation scenarios. Then, one can expect a plethora of qualitatively different propagating-front solutions - multistable, multi-periodic, quasiperiodic and chaotic.