Coexisting Hyperchaos in a Memristive Neuromorphic Oscillator

Abstract

Memristors have been widely integrated into neurons as the bridge for introducing external magnetic induction currents. The complex oscillation induced by the external magnetic stimulation is a hot topic in neuron dynamics. When a memristor is introduced into the Hindmarsh-Rose (HR) neuron to simulate the external magnetic field, a novel memristive neuromorphic hyperchaotic oscillator is constructed. The memristor weight can trigger complex neuronal firing dynamics, including the rare hyperchaotic bursting. Furthermore, when the technology of offset boosting-oriented attractor doubling is employed, a double-scroll hyperchaotic attractor can be generated, which could split into three independent coexisting attractors under some specific offsets. More interesting, two symmetric periodic attractors and two symmetric hyperchaotic attractors can coexist under certain conditions. In this work, a neuron with coexisting hyperchaotic attractors is constructed and exhaustively explored, which provides a good candidate for constituting large-scale brain-like neuromorphic oscillator. A PCB-based hardware circuit produces the oscillations validating the numerical simulations and theoretical analyses.