The Synchronization Behaviors of Memristive Synapse-Coupled Fractional-Order Neuronal Networks

The synchronization behaviors of memristive synapse-coupled fractional-order neuronal networks are investigated in this paper. Based on the integer-order memristive synapse-coupled neuronal network, a fractional-order model is proposed, and a ring network composed of fractional-order memristive synapse-coupled neuronal subnetworks is constructed. Then, the synchronization behaviors of two fractional-order memristive synapse-coupled neurons and the ring fractional-order memristive synapse-coupled neuronal network are discussed numerically. These research results suggest several novel phenomena and allow several conclusions to be drawn. For the two coupled neurons, different fractional-orders can change the threshold of memristive synapse parameter
$k_{1} $
when the two neurons are in perfect synchronization. The synchronization transitions are affected by the fractional-order and memristive synapse. Different from the integer-order model, perfect synchronization can occur before phase synchronization for some fractional-orders. Under a certain external current intensity, the transition between periodic synchronization and chaotic synchronization occurs as the fractional-order changes. The chaotic synchronization range is larger because of the memristive synapse. For the ring neuronal network coupled subnetworks, the results illustrate that the collective behaviors including incoherent, coherent, and chimera states can be induced by the fractional-order. In addition, the network’s synchronization degree is influenced by the fractional-order. The synchronization transition of the neuronal network also occurs with changes in the fractional-order.