Related papers: Mixed-Mode Oscillations in a Stochastic, Piecewise…
We analyze a biophysical model of a neuron from the entorhinal cortex that includes persistent sodium and slow potassium as non-standard currents using reduction of dimension and dynamical systems techniques to determine the mechanisms for…
We have studied the synchronization in finite $N$-unit FitzHugh-Nagumo neuron ensembles subjected to additive and multiplicative noises, by using the augmented moment method (AMM) which is reformulated with the use of the Fokker-Planck…
The use of high-frequency currents in neurostimulation has received increased attention in recent years due to its varied effects on tissues and cells. Nonlinear differential equations are commonly used as models for Neurons, and averaging…
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…
We study the nonlinear dynamics of two delay-coupled neural systems each modelled by excitable dynamics of FitzHugh-Nagumo type and demonstrate that bistability between the stable fixed point and limit cycle oscillations occurs for…
We study two identical FitzHugh-Nagumo oscillators which are coupled with one or two different time delays. If only a single delay coupling is used, the length of the delay determines whether the synchronization manifold is transversally…
We consider a system of nonlinear partial differential equations with stochastic dynamical boundary conditions that arises in models of neurophysiology for the diffusion of electrical potentials through a finite network of neurons.…
Sliding motion is evolution on a switching manifold of a discontinuous, piecewise-smooth system of ordinary differential equations. In this paper we quantitatively study the effects of small-amplitude, additive, white Gaussian noise on…
Many physical, chemical and biological systems have an inherent discrete spatial structure that strongly influences their dynamical behaviour. Similar remarks apply to internal or external noise, as well as to nonlocal coupling. In this…
The stochastic FitzHugh-Nagumo model with time delayed-feedback is often studied in excitable regime to demonstrate the time-delayed control of coherence resonance. Here, we show that the impact of time-delayed feedback in the…
Dynamics of FitzHugh-Nagumo (FN) neuron ensembles with time-delayed couplings subject to white noises, has been studied by using both direct simulations and a semi-analytical augmented moment method (AMM) which has been proposed in a recent…
The creation and subsequent evolution of marginally-unstable modes have been observed in a wide range of fusion devices. This behaviour has been successfully explained, for a single frequency shifting mode, in terms of phase-space…
We study the noisy dynamics of two coupled bistable modes of a nanomechanical beam. When de-coupled, each driven mode obeys the Duffing equation of motion, with a well-defined bistable region in the frequency domain. When both modes are…
We propose a nonlinear one-dimensional FitzHugh--Nagumo neuronal model with an asymmetric potential driven by both a high-frequency and a low-frequency signal. Our numerical analysis focuses on the influence of a state-dependent time delay…
We present recent results on noise-induced transitions in a nonlinear oscillator with randomly modulated frequency. The presence of stochastic perturbations drastically alters the dynamical behaviour of the oscillator: noise can wash out a…
In this paper, we provide a complete mathematical construction for a stochastic leaky-integrate-and-fire model (LIF) mimicking the interspike interval (ISI) statistics of a stochastic FitzHugh-Nagumo neuron model (FHN) in the excitable…
We examine the effects of pure additive noise on spatially extended systems with quadratic nonlinearities. We develop a general multiscale theory for such systems and apply it to the Kuramoto-Sivashinsky equation as a case study. We first…
Using methods of numerical simulation, we demonstrate the constructive role of memristive coupling in the context of the travelling wave formation and robustness in an ensemble of excitable oscillators described by the FitzHugh-Nagumo…
Mixed mode oscillatory (MMO) systems are known to exhibit some generic features such as the reversal of period doubling sequences and crossover to period adding sequences as bifurcation parameters are varied. In addition, they exhibit a…
We focus on the qualitative analysis of the phase portraits arising in the three-parameter FitzHugh-Nagumo system and its compactified form. The investigation is split into three parameter-dependent cases. In one of these cases, the system…