Universal Scaling of Wave Propagation Failure in Arrays of Coupled Nonlinear Cells

Abstract

We study the onset of the propagation failure of wave fronts in systems of coupled cells. We introduce a new method to analyze the scaling of the critical external field at which fronts cease to propagate, as a function of intercellular coupling. We find the universal scaling of the field throughout the range of couplings, and show that the field becomes exponentially small for large couplings. Our method is generic and applicable to a wide class of cellular dynamics in chemical, biological, and engineering systems. We confirm our results by direct numerical simulations.

4 pages, 3 figures, RevTeX

References in corpus (3)

• Tunable Pinning of Burst-Waves in Extended Systems with Discrete Sources
• Helicoidal instability of a scroll vortex in three-dimensional reaction-diffusion systems
• Perturbation analysis of weakly discrete kinks

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• Dynamics of Kinks in One- and Two- Dimensional Hyperbolic Models with Quasi-Discrete Nonlinearities
• Exact expression for the propagating front velocity in nonlinear discrete systems under nonreciprocal coupling
• Breaking chirality in nonequilibrium systems on the lattice
• Depinning transitions in discrete reaction-diffusion equations