The stability of propagating chemical spike structures and the transition to traveling pulses Original Research Article

Chemical spike structures were obtained in a special asymptotic limit of a reaction-diffusion model. Both static and propagating spike solutions of the reaction-diffusion equations were obtained. In a former paper, the static spikes were shown to be stable below a critical value qc of a certain rate coefficient q, and unstable above qc. We now extend the study to propagating spikes. Using linear stability analysis we arrive at an expression for the stability eigenvalue (or growth rate) z. The latter is found to be real for all q, and is negative between qc and 2qc and positive elsewhere. Because we know that the propagating solutions exist only for q0 over their domain of existence). The profile of the perturbed concentration has the shape of another spike-type pattern: the pulse. The results are compared with various studies on impulses and spikes most notably in nerve conduction systems. Another consequence of the study is that the model supports the existence of a single stable static spike below qc.