Neuromorphic dynamics near the edge of chaos in memristive neurons

Because of the physical limits of Moore's Law and von Neumann computing architecture, neuromorphic computing becomes a better choice to process information. The memristor, as a great candidate for the neuromorphic device, can emulate neuromorphic functions. In order to study the neuromorphic dynamics of memristive neurons, this paper proposes a tri-stable locally active memristor model via Chua's unfolding principle. The second-order and third-order memristive circuits are established by connecting energy-storage elements (inductor or capacitor) via the Hopf bifurcation and edge of chaos theorem. We further demonstrate that the memristive circuits can produce multiple kinds of neuromorphic patterns on the RHP domain near the edge of chaos, such as resting states, self-sustained oscillations, chaos, phasic bursting behaviors, burst-number adaption behaviors, refractory period behaviors, spike latency behaviors, all-or-nothing firing behaviors, tonic spiking behaviors, phasic spiking behaviors, and coexisting behaviors. Thus, this kind of memristive circuits can be considered as memristive neurons because of its neuromorphic functions.