Spontaneous Spirals in Spatial Systems

Abstract

Several chemical and biological systems produce spontaneous spirals in their dynamical behavior, such as the Belousov-Zhabotinsky reaction in chemistry and the slime mold Dictyostelium in biology. In a previous study, such spiral wave formation was accurately replicated with a computational spatial system known as the Ideal Storage Cellular Automaton Model (ISCAM). Here, a more detailed investigation is presented of the ability of this model to generate spontaneous spirals depending on its parameter values. A dynamical systems analysis is performed, and bifurcation diagrams, phase space diagrams, and snapshots of the model's spatial dynamics are presented for a range of parameter values. This analysis reveals that spiral waves can only be sustained in the system when the parameter values of the model fall well within the regime of a so-called Neimark-Sacker bifurcation.