Dynamics of a two-neuron hopfield neural network: Memristive synapse and autapses and impact of fractional order

There are numerous studies on Hopfield neural networks with electromagnetic induction using memristors in either autaptic or synaptic connections. In this study, we explore a novel scenario where all connections are influenced by electromagnetic induction. We investigate and compare the network's dynamics with one memristive autapse, two memristive autapses, and a memristive synapse. The results indicate that having two memristive autapses instead of one increases the dynamical range, leading to chaotic dynamics in unequal autaptic strengths. In contrast, in the presence of the memristive synapse, chaos can emerge only in very strong synaptic strength. Using fractional-order derivatives can transform the periodic attractor of the integer-order model into a chaotic one in some parameters. Furthermore, incorporating more memristors leads to chaos at lower fractional orders.