Competition Induced Spontaneous Resonant Annihilation of Turing Pattern

TL;DR

This paper investigates how competition among chemical species in a modified Gray-Scott model induces spontaneous resonant oscillations in Turing patterns, leading to pattern invasion and eventual annihilation.

Contribution

It reveals a novel resonant oscillation mode during pattern invasion in reaction-diffusion systems, highlighting intrinsic frequencies linked to pattern parameters.

Findings

Resonant oscillations occur during pattern invasion.

Resonant frequency depends on control parameters.

Pattern annihilation involves chaotic oscillatory behavior.

Abstract

Including an extra reactant in the Gray-Scott reaction-diffusion model, the dynamical competition between different chemical species during the Turing pattern formation can lead to species territory invasion phenomenon among different patterns of respective species. We report a peculiar oscillatory change on respective mass of a 2D pattern under competition condition by numerical simulation. The invaded Turing spot pattern can turn from a steady fading mode into a spontaneous resonant oscillation mode, the firefly lighting mode, which occurs synchronously among nearest neighboring spots, until the largest spot is annihilated finally. Such resonant oscillation behavior for annihilation can continue but in a more chaotic way towards final dying of the pattern by invasion of another pattern. The resonant frequency is found to be intrinsic character of the invaded pattern, depending on its control parameters.