Localized pattern formation: Semi-strong interaction asymptotic analysis for three components model
Publication Name
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Abstract
We investigate a three-component system involving the Belousov-Zhabotinsky reaction in water-in-oil microemulsions. Our goal is to investigate the connection between homoclinic snaking and semi-strength interaction in a three-variable reaction-diffusion system. A two-parameter bifurcation diagram of homogeneous, periodic and localized patterns is obtained numerically, and a natural asymptotic scaling for semi-strong interaction theory is found where an activator source term a=O(δ1) and b=O(δ1), with δ1 ≪ 1 being the diffusion ratio. Under this regime, singular perturbation techniques are used to construct localized steady-state patterns, and new types of non-local eigenvalue problems (NLEP) are derived to determine the stability of these patterns to O(1) time-scale instabilities. We extend the scope of the NLEP by considering a general scenario where both time-scaling parameters are non-zero. All analytical results are found to agree with numerics. Further numerical results are presented on the location of various types of breathing Hopf instability for localized patterns.
Open Access Status
This publication is not available as open access
Volume
480
Issue
2281
Article Number
20230591