Synchronization Patterns in Geometrically Frustrated Turing Rings

Abstract

Coupled nonlinear oscillators can exhibit a wide variety of patterns. We study the Brusselator as a prototypical autocatalytic reaction diffusion model. Working in the limit of strong nonlinearity provides a clear timescale separation that leads to a canard explosion in a single Brusselator. In this highly nonlinear regime it is numerically found that rings of coupled Brusselators do not follow the predictions from Turning analysis. We find that the behavior can be explained using a piecewise linear approximation.

15 Pages, 10 Figures, 2 Tabels

References in corpus (1)

• Dynamical order, disorder and propagating defects in homogeneous system of relaxation oscillators

Cited by in corpus (3)

• Hysteresis and synchronization processes of Kuramoto oscillators on high-dimensional simplicial complexes with the competing simplex-encoded couplings
• Collective dynamics of phase-repulsive oscillators solves graph coloring problem
• Emergence of long-term rhythmicity within a frustrated triangle oscillator-network