Memristor-Based Adaptive Coupling for Consensus and Synchronization

A configuration of two memristors connected with opposite polarity is proposed to realize an adaptive law for consensus and synchronization. This configuration allows one to couple two systems so that the memristor memory variables regulate the coupling strength and dynamically evolve as a function of the mismatches between the units. A physical-based model capturing the main feature of TiO₂ memristors is used for our study. Adaptive consensus of two integrators and adaptive synchronization of two chaotic circuits are investigated, and, then, extended to the case of more than two units coupled into a network configuration. The approach provides an effective strategy for the analog implementation of adaptive laws at the circuit level, as the proposed coupling configuration consists of only two components.