The stability of localized spikes for the 1-D Brusselator reaction–diffusion model

摘要: In a one-dimensional domain, the stability of localized spike patterns is analysed for two closely related singularly perturbed reaction–diffusion (RD) systems with Brusselator kinetics. For first system, where there no influx inhibitor on domain boundary, asymptotic analysis used to derive non-local eigenvalue problem (NLEP), whose spectrum determines linear multi-spike steady-state solution. Similar previous NLEP analyses other RD systems, such as Gierer–Meinhardt and Gray–Scott models, solution can become unstable either competition or an oscillatory instability depending parameter regime. An explicit result threshold value initiation instability, which triggers annihilation spikes in pattern, derived. Alternatively, regime when Hopf bifurcation occurs, it shown from numerical study that asynchronous, rather than synchronous, amplitudes be dominant instability. The existence robust asynchronous temporal oscillations has not been predicted studies systems. second boundaries, quasi-steady-state two-spike pattern reveals possibility dynamic bifurcations leading It novel mode again both detailed results theory are confirmed by extensive computations full partial differential equations system.