Firing activities in a fractional-order Hindmarsh–Rose neuron with multistable memristor as autapse

Abstract

Considering the fact that memristors have the characteristics similar to biological synapses, a fractional-order multistable memristor is proposed in this paper. It is verified that the fractional-order memristor has multiple local active regions and multiple stable hysteresis loops, and the influence of fractional-order on its nonvolatility is also revealed. Then by considering the fractional-order memristor as an autapse of HR neuron model, a fractional-order memristive neuron model is developed. The effects of the initial value, external excitation current, coupling strength and fractional-order on the firing behavior are discussed by time series, phase diagram, Lyapunov exponent and inter spike interval (ISI) bifurcation diagram. Three coexisting firing patterns, including irregular A-periodic bursting, A-periodic bursting and chaotic bursting, dependent on the memristor initial values, are observed. It is also revealed that the fractional-order can not only induce the transition of firing patterns, but also change the firing frequency of the neuron. Finally, a neuron circuit with variable fractional-order is designed to verify the numerical simulations.

Adomian Decomposition, Firing Change Process Analysis and Synchronous Control of Fractional-Order Hindmarsh–Rose Neurons in Electromagnetic Field

“…S(t) = 0 on the sliding surface, so e 1 = −e 3 . On the other hand, D α t e 3 = −e 1 is obtained according to the third equation of formula (13), so e 3 → 0, e 1 → 0.…”

“…Wang et al [12] studied the dynamic response and stochastic resonance of electrical activity under the influence of electromagnetic induction and white noise in the Hodgkin-Huxley (H-H) model. Li et al [13], according to the HR neuron model, constructed a fractional-order HR memristive neuron model, and analyzed the multistable behavior of the model by using tools such as an attraction basin and phase diagram.…”

Synchronization and firing mode transition of two neurons in a bilateral auditory system driven by a high–low frequency signal

“…[10][11][12] When a memristor is connected to a neural circuit, the impact of electromagnetic induction on neurons can be estimated. [5,[13][14][15][16] Because the resistance value of a thermistor varies with temperature, [17][18][19][20] neural circuits with thermistors can be used as biophysical thermosensitive neurons. [21][22][23][24] Phototubes can convert optical signals into electrical signals.…”

Fractional-order heterogeneous memristive Rulkov neuronal network and its medical image watermarking application

“…[2,3] Studying the chaotic dynamics of the nervous system, a vital step to comprehend the origin of neuronal diseases, holds significant theoretical and practical implications. [4] To study and emulate the critical dynamic characteristics of neurons, several mathematical models have been established by researchers, which encompass the Hindmarsh-Rose (HR) model, [5] FitzHugh-Nagumo (FHN) model, [6] Rulkov model, [7,8] and the Izhikevich model. [9] The development and application of these models significantly advance the field of neurophysiology, which contribute to a deeper understanding of the complex dynamics of the human brain.…”