Edge of Chaos in Reaction-Diffusion System with Memristor Synapses

In this paper principles of local activity theory will be presented for studying complex behavior of reaction-diffusion systems. For reaction-diffusion models, one can determine the domain of the cell parameters in order for the cells to be locally active, and thus potentially capable of exhibiting complexity. In the literature, the so called edge of chaos (EC) means a region in the parameter space of a dynamical system, where complex phenomena and information processing can emerge. In this paper edge of chaos domain will be determined for a reaction-diffusion model with memristor synapses. In our model each cell will be arranged on a two-dimensional square grid and will be connected to adjacent cells through coupling devices that mimic 2-D spatial diffusion and transmit the cell’s state to its neighboring cells. Numerical simulations will illustrate the obtained theoretical results.