Abstract
A model is introduced by coupling two three-dimensional Hindmarsh-Rose models with the help of a nonsmooth memristor. The firing patterns dependent on the external forcing current are explored, which undergo a process from adding-period to chaos. The stability of equilibrium points of the considered model is investigated via qualitative analysis, from which it can be gained that the model has diversity in the number and stability of equilibrium points for different coupling coefficients. The coexistence of multiple firing patterns relative to initial values is revealed, which means that the referred model can appear various firing patterns with the change of the initial value. Multiple firing patterns of the addressed neuron model induced by different scales are uncovered, which suggests that the discussed model has a multiscale effect for the nonzero initial value.
Highlights
As the building elements of the nervous system, the neuron is the most fundamental unit in neural processing
Other simplified neuron models were proposed successively, which mainly explained lots of ion channels, various synapses, and spatial geometry of individual cells, such as the FitzHughNagumo (FHN) model [2] depicting a prototype of a neuron, the Hindmarsh-Rose (HR) model [3] simulating the characteristics of neurons in the hippocampus of the brain, the Morris-Lecar (ML) model [4] obtained in the research on muscle fiber of Arctic goose, the Chay model [5] as a new theoretical model with unity based on many different types of excitable cells, and the Izhikevich neuron model [6] regarded as a mathematical simplification of the HH model using a binary tree
The FHN neuron model exhibits discontinuous transition between different oscillations [7] and double coherence resonance induced by phase noise [8]; the HH neuron model displays evoking spiking caused by enough noise intensity [9], chaotic resonance dependent on current intensity [10], and extrinsic stochastic resonance caused by ion shot noise [11]; in the presence of periodic input, the HR neuron model can show nonlinear resonance behavior [12], periodic and chaotic firing patterns [13], transition between chaotic firing and periodic firing [14], and bursting phenomenon [15]; the Izhikevich neuron model can appear chaotic resonance [16, 17]; the ML neuron model can exhibit mono- and bistable dynamic regimes [18] and responses to two temperature-sensitive ion channels, calcium and leak current, respectively [19]
Summary
As the building elements of the nervous system, the neuron is the most fundamental unit in neural processing. The FHN neuron model exhibits discontinuous transition between different oscillations [7] and double coherence resonance induced by phase noise [8]; the HH neuron model displays evoking spiking caused by enough noise intensity [9], chaotic resonance dependent on current intensity [10], and extrinsic stochastic resonance caused by ion shot noise [11]; in the presence of periodic input, the HR neuron model can show nonlinear resonance behavior [12], periodic and chaotic firing patterns [13], transition between chaotic firing and periodic firing [14], and bursting phenomenon [15]; the Izhikevich neuron model can appear chaotic resonance [16, 17]; the ML neuron model can exhibit mono- and bistable dynamic regimes [18] and responses to two temperature-sensitive ion channels, calcium and leak current, respectively [19].
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