Coupling dynamics of locally active memristor based neurons

Brain-like dynamics require third-order or higher-order complexity. In order to investigate the coupling neuromorphic behaviors of identical third-order memristive neurons, this paper begins with the aim of exploring two identical neuron based dynamics under distinct operating regimes and coupling strengths. Without coupling, the single neuron can exhibit resting states, periodic spikes, or chaos depending on the bias condition. The uncoupled resting neurons can be activated by resistive coupling, inducing inhomogeneous resting states (static Smale paradox) and inhomogeneous spikes (dynamic Smale paradox) due to the edge of chaos regime. Considering the single neuron at the periodic spikes or chaotic states, the coupled neurons can mimic shocking oscillation death, non-periodic asynchronization, and periodic synchronization via the Hopf bifurcation theory. From the above analyses, an artificial ring neural network is constructed using 100 memristive neurons and resistive synapses to further study the coupled mechanism, generating exotic spatiotemporal patterns such as chimera death, amplitude chimera, solitary states, and asynchronization because of symmetry breaking. This sheds new light on exploring exotic spatiotemporal patterns of networks based on memristive neurons from the perspective of the nonlinear circuit theory.