Turing patterns in the simplest MCNN

Abstract

Complex patterns can be often retrieved in spatially-extended systems formed by coupled nonlinear dynamical units. In particular, Turing patterns have been extensively studied investigating mathematical models related to different contexts, such as chemistry, physics, biology, and also mechanics and electronics. In this paper, we focus on the emergence of Turing patterns in a circuit architecture formed by coupled units in which a memrsitive element is considered. Furthermore, the unit is formed by only two elements, namely a capacitor and a memristor. The analytical conditions for which Turing patterns can be obtained in the proposed architecture are discussed in order to inform the design of the circuit parameters. Moreover, the characterization of the different types of patterns is performed with respect to the strength of the diffusion occurring between the units. Finally, it is worth to note that the proposed architecture can be considered as the simplest electronic circuit able to undergo Turing instability and give rise to pattern formation.