The FitzHugh–Nagumo model describing propagation of nerve impulses in axons is given by fast-slow reaction-diffusion equations, with dependence on a parameter representing the ratio of time scales. It is well known that for all sufficiently small > 0 the system possesses a periodic traveling wave. With the help of computer-assisted rigorous computations, we prove the existence of this periodic ...

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 prove the validity of an averaging principle for a class of systems of slow-fast reaction-diffusion equations with the reaction terms in both equations having polynomial growth, perturbed by a noise of multiplicative type. The models we have in mind are the stochastic Fitzhugh– Nagumo equation arising in neurophysiology and the Ginzburg–Landau equation arising in statistical mechanics.

We study numerically the Turing pattern in three dimensions in a FitzHugh-Nagumo-type reaction-diffusion system. We have found that interconnected periodic domain structures such as a gyroid, Fddd, and perforated lamellar structures appear in three dimensions, which never exist in lower dimensions. The stability analysis of these structures is also performed by means of a mode expansion.

We provide a convergence result for numerical schemes approximating nonlocal front propagation equations. Our schemes are based on a recently investigated notion of weak solution for these equations. We also give examples of such schemes, for a dislocation dynamics equation, and for a Fitzhugh-Nagumo type system.

We present explicit and online Model Predictive Controllers (MPCs) for an excitable cell simulator based on the nonlinear FitzHugh-Nagumo model. Despite the plant’s nonlinearity, we are able to formulate the model predictive control problem as an instance of quadratic programming, using a PieceWise Affine (PWA) abstraction of the plant. The speed-versus-accuracy tradeoff for the explicit and on...