Wave Propagation and Wave Pattern Formation in Nonuniform Reaction-Diffusion Systems

Abstract

The study of wave propagation and pattern formation in two- and three- dimensional reaction-diffusion systems (RDS) has progressed significantly during the past 25 years since the introduction of homogeneous, isothermal, excitable chemical media [1–6]. While the most basic properties of chemical waves have been studied in spatially uniform systems, the wave propagation in nonuniform ones is also of considerable interest, because natural reaction-diffusion media such as biological excitable tissues and ecological systems are strongly nonuniform. In uniform systems only symmetry-breaking initial conditions give rise to new patterns [7]; nonuniformities and gradients of concentrations and other local parameters of media bring with them an initial asymmetry, which generates new routes for pattern formation and permits the emergence of new types of wave patterns.