THE STABILITY OF STATIC CHEMICAL SPIKE STRUCTURES IN REACTION DIFFUSION-SYSTEMS

Under certain conditions, reaction-diffusion systems can support spike structures. According to the adopted model, both static and propagating chemical spike solutions exist below a critical value q(c) of a certain rate parameter q. Above q(c), only static spikes exist. A linear analysis is carried out here to investigate the stability of these structures. A general relation between the stability eigenvalue z and the rate factor q is obtained. The problem is then solved for static spikes. The latter are shown to be stable only for q < q(c), implying that the static spike solutions shown to exist for q > q(c) are unstable. There exists a value of q for which the static spikes exhibit maximum stability.