Forced symmetry breaking as a mechanism for rogue bursts in a dissipative nonlinear dynamical lattice.

Abstract

We propose an alternative to the standard mechanisms for the formation of rogue waves in a nonconservative, nonlinear lattice dynamical system. We consider an ordinary differential equation (ODE) system that features regular periodic bursting arising from forced symmetry breaking. We then connect such potentially exploding units via a diffusive lattice coupling and investigate the resulting spatiotemporal dynamics for different types of initial conditions (localized or extended). We find that in both cases, particular oscillators undergo extremely fast and large amplitude excursions, resembling a rogue wave burst. Furthermore, the probability distribution of different amplitudes exhibits bimodality, with peaks at both vanishing and very large amplitude. While this phenomenology arises over a range of coupling strengths, for large values thereof the system eventually synchronizes and the above phenomenology is suppressed. We use both distributed (such as a synchronization order parameter) and individual oscillator diagnostics to monitor the dynamics and identify potential precursors to large amplitude excursions. We also examine similar behavior with amplitude-dependent diffusive coupling.