A system of ODE’s is used to attempt an approximation of the dynamics of two delayed coupled FitzHugh-Nagumo excitable units, described by delay-differential equations. It is shown that the codimension 2 generalized Hopf bifurcation acts as the organizing center for the dynamics of ODE’s for small time-lags. Furthermore, this is used to explain important qualitative properties of the exact dyna...

An application of the Exp-function method to search for exact solutions of nonlinear differential equations is analyzed. Typical mistakes of application of the Exp-function method are demonstrated. We show it is often required to simplify the exact solutions obtained. Possibilities of the Exp-function method and other approaches in mathematical physics are discussed. The application of the sing...

Abstract. The purpose of the paper is to show that analogue electronic modelling is an extremely fast technique compared to conventional digital computing, especially when solving large sets of coupled nonlinear differential equations. An array of thirty FitzHugh–Nagumo type electronic oscillators, modelling dynamics of the brain neurons, is considered. The decrease of time consumption by a fac...

We analyze a piecewise-linear FitzHugh-Nagumo model. The system exhibits a canard near which both small amplitude and large amplitude periodic orbits exist. The addition of small noise induces mixed-mode oscillations (MMOs) in the vicinity of the canard point. We determine the effect of each model parameter on the stochastically driven MMOs. In particular we show that any parameter variation (s...

Using a model system of FitzHugh-Nagumo type in the excitable regime, the similarity between synchronization of self-sustained and noise-induced oscillations is studied for the case of more than one main frequency in the spectrum. It is shown that this excitable system undergoes the same frequency lockings as a self-sustained quasiperiodic oscillator. The presence of noise-induced both stable a...

We have identified the occurrence of chimera states for various coupling schemes in networks of two-dimensional and three-dimensional Hindmarsh-Rose oscillators, which represent realistic models of neuronal ensembles. This result, together with recent studies on multiple chimera states in nonlocally coupled FitzHugh-Nagumo oscillators, provide strong evidence that the phenomenon of chimeras may...

-Measurements of the normalized radar cross section (_o) made by the YSCAT nltrawideband scatterometer during an extended deployment on the Canada Centre for Inland Waters (CCIW) Research Tower located at Lake Ontario are analyzed and compared with anemometer wind measurements to study the sensitivity of cr° to the wind speed as a function of the Bragg wavelength. This paper concentrates on upw...

A gradient particle method is used to compute probability densities for processes with delay bifurcations that are sensitive to very small noise. The method is particularly useful for computing the probability density in the transition region, where asymptotic approximations may not be valid. For a one dimensional steady bifurcation problem and a two-dimensional FitzHugh-Nagumo model we solve t...

The reaction-diffusion system of Fitzhugh Nagumo is considered. The initialboundary problems with Neumann and Dirichlet conditions are analyzed. By means of an equivalent semilinear integrodifferential equation which characterizes several dissipative models of viscoelasticity, biology, and superconductivity, some results on existence, uniqueness and a priori estimates are deduced both in the li...

The Nagumo-Sato (NS) model is a one-dimensional piecewise linear map that describes simplified dynamics of a single neuron. The NS model and its network extension, coupled Nagumo-Sato models, exhibit complex behavior both in their transient dynamics and after converging to periodic orbits. However, the way the period and the transient length change against the parameters is not completely under...