Front propagation into unstable states in discrete media

2016/05/02 by K. Alfaro-Bittner, Marcel G. Clerc, Alfaro-Bittner, K. +5
Computer Science · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Nonlinear Dynamics and Pattern Formation #Pattern Formation and Solitons (nlin.PS) #Spectroscopy and Quantum Chemical Studies

paper · pdf · doi:10.48550/arxiv.1605.00556

openalex publication_date 2016/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Non-equilibrium dissipative systems usually exhibit multistability, leading to the presence of propagative domain between steady states. We investigate the front propagation into an unstable state in discrete media. Based on a paradigmatic model of coupled chain of oscillators and populations dynamics, we calculate analytically the average speed of these fronts and characterize numerically the oscillatory front propagation. We reveal that different parts of the front oscillate with the same frequency but with different amplitude. To describe this latter phenomenon we generalize the notion of the Peierls-Nabarro potential, achieving an effective continuous description of the discreteness effect.

Citations

• Pattern formation outside of equilibrium

Related

• Front propagation close to the onset of instability
• Stable transport of information near essentially unstable localized structures
• Exact expression for the propagating front velocity in nonlinear discrete systems under nonreciprocal coupling
• Travelling Fronts, Pulses, and Pulse Trains in a 1D discrete Reaction-Diffusion System
• Propagation of stationary exothermic transition front with nonstationary oscillatory tail