Firing modes of a memristive complex-valued FHN neuron

Abstract

Memristors have been extensively integrated into neurons as key elements for emulating electromagnetic radiation (EMR). The complex firing patterns triggered by external magnetic field is a hot topic in neuronal dynamics. By integrating a specially designed memristor into a complex-valued FitzHugh–Nagumo (CV-FHN) neuron model to emulate external magnetic induction current, we have developed a novel neuromorphic system. Our findings reveal that hidden scroll-controlled chaotic attractors can be generated from the neuromorphic system through adjustment of the memristor parameter, while the offset of heterogeneous coexisting attractors in the phase space can be boosted by modifying the initial conditions of the memristor. Moreover, the Hamilton energy function of the neuron is calculated by using Helmholtz’s theorem. The results of Hamilton energy analysis indicate that various hidden firing patterns, including hidden chaotic spiking and even hyperchaotic bursting, can be modulated by external stimuli. In this work, the introduction of memristor into CV-FHN neuron significantly enhances the chaos complexity of neuronal firing dynamics of the original neuron. This memristive CV-FHN neuron serves as a promising candidate for constituting large-scale functional neural network.