We prove local existence of solutions for a class of suitably renormalised coupled SPDE–ODE systems driven by space-time white noise, where the space dimension is equal to 2 or 3. This class includes in particular the FitzHugh–Nagumo system describing the evolution of action potentials of a large population of neurons, as well as models with multidimensional gating variables. The proof relies o...

Abstract 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 each of the parameters to some statistics from spiketime data. Using these formulae, each parameter is inferred from a specific set of statistics. W...

Introduction: Hyperandrogenism may be implicated in the pathogenesis of pre-eclampsia. We hypothesised that there may be a difference between the levels of testosterone in pregnant women complicated with pre-eclampsia and those of matched women without this complication. Material and methods: A case-control study conducted in Tehran, Iran between January and June 2006 included 20 women with mod...

We study the regularity of noise-induced excitations in the FitzHugh–Nagumo (FHN) neuronal model subject to excitatory and inhibitory high-frequency input with and without correlations. For each value of the correlation a relative maximum of spike coherence can be observed for intermediate noise strengths (coherence resonance). Moreover, the FHN system exhibits an absolute maximum of coherent s...

The divergence criterion has been shown to be helpful in distinguishing between suband supercritical Hopf bifurcations but its applicability is limited to systems whose divergence is sign definite. A step by step computational procedure which allows one to extend the applicability of the divergence criterion is derived by altering the system to an equivalent one with sign definite divergence. T...

We investigated self-organized patterns formed by a FitzHugh–Nagumo model in three-dimensional space. We found functional orders in the model. The edge plane structure was autonomously extracted from an initial cubic pattern. As in a two-dimensional model, the edge points and edge lines developed spontaneously in this model. These edge structures were obtained when parameters were in a specific...

This paper presents a multistable discrete memristor that is based on the discretization of continuous-time model. It has been observed model capable preserving characteristics continuous Furthermore, three-dimensional discrete-time FitzHugh–Nagumo constructed by integrating into two-dimensional (FN) neuron Subsequently, dynamic behavior proposed analyzed through Lyapunov exponents, phase portr...

This thesis considers a stochastic dynamical system that has multiple time scales. The focus lies on the planar slow-fast stochastic differential equation (a singularly perturbed stochastic system) modeling the spiking activity of an isolated FitzHugh-Nagumo neural oscillator. We analyze the model equation on the slow time scale τ (Eq.(1)) and on the fast time scale t (Eq.(2)). { dvτ = ε f(vτ ,...