Oscillatory and chaotic dynamics in compartmentalized geometries.

Abstract

The effects of spatial compartmentalization of a multistep reaction mechanism (Willamowski-Rössler model) whose mass action rate law shows oscillations and chaotic dynamics are explored. The mechanism is decomposed into subsets of reactions that are then assumed to take place in distinct regularly or randomly distributed spatial domains in the system. The reactive domains are coupled by diffusion. The spatiotemporal system states are investigated as a function of the system size and geometrical arrangement of the domains. A compartmentalization is chosen where the isolated domain attractors are simple steady states. It is then shown that changes in the system size or domain geometry can produce bifurcations leading to simple or period-doubled oscillatory attractors as well as chaotic states. These bifurcations are analyzed by direct simulations of the compartmentalized reaction-diffusion equations and by an analysis in terms of integral equations.