Capacitively Coupled Memristive Neurons on the Edge of Chaos

Edge of chaos is characterized by the stability accompanied with potential instability, and plays an important role in the research of memristive neuron circuits. In this brief, we investigate the dynamics of two identical
${\mathrm{ NbO}}_{\mathrm{ x}}$
memristive neurons under capacitive coupling. Before coupled, both two memristive neurons show resting states, which originate from edge of chaos. After capacitively coupled, these two neurons can fire complex neuromorphic behaviors, such as tonic spiking, bursting, and even chaos. Based on the small signal analysis method, Hopf bifurcation, and edge of chaos theory, the activation condition of coupled neurons is quantitatively presented. Moreover, coexisting phenomena of stable equilibrium point and stable limit cycle also emerge in this coupled network, which is caused by the subcritical Hopf bifurcation. The simulation results verify the correctness of the proposed analysis method and demonstrate that the developed coupled memristive neurons have rich dynamics.