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...

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...

The aim of this work is to investigate the dynamics of a neural network, in which neurons, individually described by the FitzHugh-Nagumo model, are coupled by a generalized diffusive term. The formulation we are going to exploit is based on the general framework of graph theory. With the aim of defining the connection structure among the excitable elements, the discrete Laplacian matrix plays a...

Statistical complexity measures are used to detect noise-induced order and to quantify stochastic and coherence resonances. We illustrate the method with two paradigmatic models, one of a Brownian particle in a sinusoidally modulated bistable potential, and the other, the FitzHugh-Nagumo model of excitable systems. The method can be employed for the precise detection of subtle signatures of noi...

The paper deals with a semilinear integrodifferential equation that characterizes several dissipative models of Viscoelasticity, Biology and Superconductivity. The initial boundary problem with Neumann conditions is analyzed. When the source term F is a linear function, then the explicit solution is obtained. When F is non linear, some results on existence, uniqueness and a priori estimates are...

Despite of the pain and limited accuracy of blood tests for early recognition of cardiovascular disease, they dominate risk screening and triage. On the other hand, heart rate variability is non-invasive and cheap, but not considered accurate enough for clinical practice. Here, we tackle heart beat interval based classification with deep learning. We introduce an end to end differentiable hybri...

Viability and invariance problems related to a stochastic equation in a Hilbert space H are studied. Finite dimensional invariant C submanifolds of H are characterized. We derive Nagumo type conditions and prove a regularity result: Any weak solution, which is viable in a finite dimensional C submanifold, is a strong solution. These results are related to finding finite dimensional realizations...

A b s t r a c t . We examine the effects of changing the coefficient of variation (CV) of the inter-stimulus interval on the CV of the output interspike interval (ISI), using constant magnitude, supra-threshold pointprocess stimuli of the membrane potential variable in the FitzHughNagumo model. The coefficient of variation of the input is changed within the context of a displaced exponential di...

We consider an idealized network, formed by N neurons individually described by the FitzHugh-Nagumo equations and connected by electrical synapses. The limit for N → ∞ of the resulting discrete model is thoroughly investigated, with the aim of identifying a model for a continuum of neurons having an equivalent behaviour. Two strategies for passing to the limit are analysed: i) a more convention...