Dynamical behavior and applications of fractional-order bicyclic crossed memristive neural networks with...

This study proposes a fractional-order NbO_x memristor model and, based on this, introduces a novel fractional-order bicyclic crossed memristive neural network. The dynamic behaviors and firing patterns of this neural network are analyzed, with an emphasis on the Neimark-Sacker bifurcation induced by the fractional-order parameter: it is demonstrated that by keeping the system parameters constant and varying only the fractional order, a Neimark-Sacker bifurcation can be induced. The chaotic characteristics and bifurcations of this network are leveraged in a newly proposed image encryption algorithm that successfully passes various security analyses. Additionally, a synchronization controller is designed to regulate the generation of specific chaotic sequences by other neural networks, with the objective of approximating the chaotic sequences produced by the proposed neural network.