An efficient, nonlinear stability analysis for detecting pattern formation in reaction diffusion systems.

摘要: Reaction diffusion systems are often used to study pattern formation in biological systems. However, most methods for understanding their behavior challenging and can rarely be applied complex common applications. I present a relatively simple efficient, nonlinear stability technique that greatly aids such analysis when rates of substantially different. This reduces system reaction equations ordinary differential tracking the evolution large amplitude, spatially localized perturbation homogeneous steady state. Stability properties this system, determined using standard bifurcation techniques software, describe both linear patterning regimes system. class method demonstrate its application. Analysis Schnakenberg substrate inhibition models is performed capabilities simplified settings show even these have not previously detected. The real power technique, however, simplicity applicability larger where other become intractable. demonstrated through chemotaxis regulatory network comprised interacting proteins phospholipids. In each case, predictions verified against results numerical simulation, stability, asymptotic, and/or full PDE analyses.