Autowaves Properties Observed in Reaction-Diffusion Cellular Neural Networks

Cellular neural network is a well-known mathematical model for investigation of deterministic, stochastic and chaotic processes in nonlinear dynamic systems. The turn to a reaction-diffusion cellular neural network (RDCNN) enables to model different types of autowave processes (concentric, circular and spiral waves, Turing structures, etc.) RDCNN is a convenient architecture for the mathematical description of the systems of nonlinear differential equations with diffusion and their solution based on numerical methods. Running circular and spiral waves in RDCNN are synthesized and their properties are demonstrated (preservation of the shape and amplitude of the running waves, as well as the destruction of waves which results from their collision.) Autowaves are built in the MATLAB system on using the fourth-order Runge–Kutta numerical method.