Large-Scale Memrisitive Rulkov Ring-Star Neural Network With Complex Spatio-Temporal Dynamics

Memristors have been employed in various continuous neural network models through emulating magnetic induction effect, but have not yet been successfully performed in discrete neural network models. To address this issue, this article first proposes a discrete memristive Rulkov neuron model (MRN) and then constructs a large-scale discrete memristive Rulkov ring-star neural network model (MRRSNN). Furthermore, spatiotemporal pattern, snapshot, and recurrence plot of the nodes are adopted to declare the spatio-temporal dynamics of the MRRSNN. Consequently, it can manifest rich network behaviors, including double-well chimera, asynchronized, multiclustered, solitary, synchronized, and continuous traveling wave states. Besides, the influence of the memristive coupling strength and initial conditions of MRNs on the network behaviors is quantified by three metrics, including root mean-square deviation, averaged cross-correlation coefficient, and normalized time-averaged synchronization error, which provides an important basis for state regulation of the MRRSNN. Finally, a spatio-temporal chaos-based pseudorandom number generator is designed, and experiment results from the NIST 800-22 and performance indicators show that the MRRSNN generates better random sequences than the MRN even in the presence of dynamic degeneracy.