Interaction of self-organized quasiparticles in a two-dimensional reaction-diffusion system: The formation of molecules

Abstract

In two-dimensional reaction-diffusion systems localized, solitary structures, that we call self-organized quasiparticles or spots, can be found as stable and stationary solutions. Combinations of two or more spots can lead to rather complex patterns, that can be understood by treating them as particles. These particles can interact with the boundaries of the system as well as with each other in different ways, that depend essentially on the parameters of the system. The interaction can be described by an approximation based on the exponential decay of the spots apart from their centers. The calculations reduce the dynamics of the system to some equations for the velocities of the spots. In particular, there is a parameter range where the interaction of two spots oscillates with their distance, which gives rise to infinitely many bounded states, resembling molecules. Investigating more than two spots molecules of numerous shapes have been obtained.