Abstract In this paper, we shall study the formation of stationary patterns for a reaction-diffusion system in which FitzHugh-Nagumo (FHN) kinetics, its excitable regime, is coupled to linear cross-diffusion terms. (Gambino et al. Excitable Fitzhugh-Nagumo model with cross-diffusion: long-range activation instabilities, 2023), proved that supports emergence cross-Turing patterns, i.e., close-to...

A simple electro-mechanical model of the heart is derived to best t available cardiac images. The model is based on anisotropic linear elasticity and, from the electrical point of view, on the nite-element discretisation of the FitzHugh-Nagumo electric wave-propagation model. Present simulations include static image segmentation. By including biological and physical a priori knowledge, more rea...

A simple electro-mechanical model of the heart is derived to best fit available cardiac images. The model is based on anisotropic linear elasticity and, from the electrical point of view, on the finite-element discretisation of the FitzHugh-Nagumo electric wave-propagation model. Present simulations include static image segmentation. By including biological and physical a priori knowledge, more...

Abstract We consider the existence and first order conditions of optimality for a stochastic optimal control problem inspired by celebrated FitzHugh–Nagumo model, with nonlinear diffusion term, perturbed linear multiplicative Brownian-type noise. The main novelty present paper relies on application rescaling method which allows us to reduce original random one.