Recent advances in the experimental and theoretical study of dynamics of neuronal
electrical firing activities are reviewed. Firstly, some experimental phenomena of neuronal …

The Hodgkin--Huxley model was developed to characterize the action potential of a squid
axon. It has served as an archetype for compartmental models of the electrophysiology of …

The aim of this study is to extend the soliton propagation model in biomembranes and
nerves constructed by Heimburg and Jackson for the case of fractal dimensions. Our …

We propose an extension of the Fitzhugh-Nagumo model, which possesses a regime of
three coexisting stable states: resting equilibrium and two stable oscillatory states. Such a …

We investigate the response characteristics of a generalized FitzHugh-Nagumo model
under an external sinusoidal current and the synchronization of two neurons coupled with a …

A recurrent loop consisting of a single Hodgkin-Huxley neuron influenced by a chemical
excitatory delayed synaptic feedback is considered. We show that the behavior of the system …

Dynamical mechanisms of the biological pacemaker (BP) generation in human ventricular
myocytes were investigated by bifurcation analyses of a mathematical model. Equilibrium …

This paper presents a two-dimensional simplified Hodgkin–Huxley model under exposure to
electric fields. The Hopf bifurcations of the simplified Hodgkin–Huxley model are …

In the past few decades, neural networks have been extensively adopted in various
applications ranging from simple synaptic memory coding to sophisticated pattern …

In a new memristive generalized FitzHugh–Nagumo bursting model, adaptive resonance
(AR), in which the neuron system's response to a varied stimulus can be improved by the …