Synchronization stability and pattern selection in a memristive neuronal network.

Spatial pattern formation and selection depend on the intrinsic self-organization and cooperation between nodes in spatiotemporal systems. Based on a memory neuron model, a regular network with electromagnetic induction is proposed to investigate the synchronization and pattern selection. In our model, the memristor is used to bridge the coupling between the magnetic flux and the membrane potential, and the induction current results from the time-varying electromagnetic field contributed by the exchange of ion currents and the distribution of charged ions. The statistical factor of synchronization predicts the transition of synchronization and pattern stability. The bifurcation analysis of the sampled time series for the membrane potential reveals the mode transition in electrical activity and pattern selection. A formation mechanism is outlined to account for the emergence of target waves. Although an external stimulus is imposed on each neuron uniformly, the diversity in the magnetic flux and the induction current leads to emergence of target waves in the studied network.