Related papers: Voltage interval mappings for an elliptic bursting…
We study the stochastic FitzHugh-Nagumo equations, modelling the dynamics of neuronal action potentials, in parameter regimes characterised by mixed-mode oscillations. The interspike time interval is related to the random number of…
We investigate a possibility of realization of structurally stable chaotic dynamics in neural systems. The considered model of interacting neurons consists of a pair of coupled FitzHugh-Nagumo systems, with the parameters being periodically…
An electronic circuit device, inspired on the FitzHugh-Nagumo model of neuronal excitability, was constructed and shown to operate with characteristics compatible with those of biological sensory neurons. The nonlinear dynamical model of…
The three-dimensional (3D) Fitzhugh-Nagumo neuron model with inertia was shown to exhibit a chaotic mixed-mode dynamics composed of large-amplitude spikes separated by an irregular number of small-amplitude chaotic oscillations. In contrast…
Being an example for a relaxation oscillator, the FitzHugh-Nagumo model has been widely employed for describing the generation of action potentials. In this paper, we begin with a biological interpretation of what the subsequent…
In this paper, the transport phenomena of synaptic electric impulses are considered. The FitzHugh--Nagumo and FitzHugh--Rinzel models appear mathematically appropriate for evaluating these scientific issues. Moreover, applications of such…
Many neuronal systems and models display a certain class of mixed mode oscillations (MMOs) consisting of periods of small amplitude oscillations interspersed with spikes. Various models with different underlying mechanisms have been…
Bifurcation analysis is applied to the FitzHugh-Nagumo oscillator driven by a sinusoidal source. A numerically generated 2d regime map showing the variety of oscillatory dynamics in the parameter space of source frequency and amplitude…
We study the phenomenological model of ensemble of two FitzHugh-Nagumo neuron-like elements with symmetric excitatory couplings. The main advantage of proposed model is the new approach to model of coupling which is implemented by smooth…
We consider a model of a square-wave bursting neuron residing in the regime of tonic spiking. Upon introduction of small stochastic forcing, the model generates irregular bursting. The statistical properties of the emergent bursting…
In this work, we explore the influence of coupling strength, network size, and randomness on the collective dynamics of FitzHugh-Nagumo oscillators on complex networks. Using Watts-Strogatz small-world network connectivities, we identify…
Chaotic bursting behaviors have been observed by many authors in neural dynamics mainly in the transition between different kinds of bursting behavior. As a well-known three-dimensional ODEs model with various bursting solutions, the…
In this paper, we study an excitable, biophysical system that supports wave propagation of nerve impulses. We consider a slow-fast, FitzHugh-Rinzel neuron model where only the membrane voltage interacts diffusively, giving rise to the…
Temporal Interference Stimulation (TIS) is a non-invasive neuromodulation technique in which two high-frequency sinusoidal currents with slightly different frequencies generate a low-frequency envelope that can activate deep neural…
Emergence of noise induced regularity or Coherence Resonance in nonlinear excitable systems is well known. We explain theoretically why the normalized variance ($V_{N}$) of inter spike time intervals, which is a measure of regularity in…
A simple model that replicates the dynamics of spiking and spiking-bursting activity of real biological neurons is proposed. The model is a two-dimensional map which contains one fast and one slow variable. The mechanisms behind generation…
Systems of FitzHugh-Nagumo units with different coupling topologies are capable of self-generating and -terminating strong deviations from their regular dynamics that can be regarded as extreme events due to their rareness and recurrent…
Human hearing range significantly surpasses the typical neuronal spiking frequency. Yet, neurons with their modest frequency range not only efficiently receive and process multiple orders higher frequency signals, but also demonstrate…
In a series of two papers, we investigate the mechanisms by which complex oscillations are generated in a class of nonlinear dynamical systems with resets modeling the voltage and adaptation of neurons. This first paper presents…
We propose theoretical methods to infer coupling strength and noise intensity simultaneously through an observation of spike timing in two well-synchronized noisy oscillators. A phase oscillator model is applied to derive formulae relating…