Turing Patterns in Memristive Cellular Nonlinear Networks

The formation of ordered structures, in particular Turing patterns, in complex spatially extended systems has been observed in many different contexts, spanning from natural sciences (chemistry, physics, and biology) to technology (mechanics and electronics). In this paper, it is shown that the use of memristors in a simple cell of a spatially-extended circuit architecture allows us to design systems able to generate Turing patterns. In addition, the memristor parameters play a key role in the selection of the type and characteristics of the emerging pattern, which is also influenced by the initial conditions. The problem of finding the regions of parameters where Turing patterns may emerge in the proposed cellular architecture is solved in an analytic way, and numerical results are shown to illustrate the system behavior with respect to its parameters.