We introduce a technique based on algebraic topology for quantifying spatio-temporally chaotic dynamics. The technique is illustrated using the Gray-Scott and the FitzHugh-Nagumo models.

We study a singularly perturbed system of partial differential equations that models a one-dimensional array of coupled Chua’s circuits. The PDE system is a natural generalization to the FitzHugh-Nagumo equation. In part I of the paper, we show that similar to the FitzHugh-Nagumo equation, the system has periodic traveling wave solutions formed alternatively by fast and slow flows. First, asymp...

The aim of this work is to describe the dynamics a fractional-order coupled FitzHugh–Nagumo neuronal model. equilibrium states are analyzed in terms their stability properties, both dependently and independently fractional orders Caputo derivatives, based on recently established theoretical results. Numerical simulations shown clarify exemplify

Using the standard van der Pol–FitzHugh–Nagumo excitable medium model, I demonstrate a generic mechanism, diversity, that provokes the emergence of global oscillations from individually quiescent elements in heterogeneous excitable media. This mechanism may be operating in the mammalian pancreas, where excitable b cells, quiescent when isolated, are found to oscillate when coupled, despite the ...

This article focuses on the qualitative analysis of complex dynamics arising in a few mathematical models neuroscience context. We first discuss three-dimensional FitzHugh–Rinzel (FHR) model and then illustrate those class non-homogeneous FitzHugh–Nagumo (Nh-FHN) reaction-diffusion systems. FHR Nh-FHN can be used to generate relevant wave-propagation phenomena Such include canards, mixed-mode o...

In the study, the activation propagation velocity in cardiac tissue was simulated in COMSOL Multiphysics environment using the modified FitzHugh-Nagumo model of the electrical excitation. The influence of different model parameters and stimulation conditions on the activation propagation velocity was evaluated. The homogeneous slab model was used as the model of the atrial wall. Results of simu...

We develop a data-driven method, based on semi-supervised classification, to predict the asymptotic state of multistable systems when only sparse spatial measurements system are feasible. Our method predicts behavior an observed by quantifying its proximity states in precomputed library data. To quantify this proximity, we introduce sparsity-promoting metric-learning (SPML) optimization, which ...

Using the standard van der Pol-FitzHugh-Nagumo excitable medium model, I demonstrate a generic mechanism, diversity, that provokes the emergence of global oscillations from individually quiescent elements in heterogeneous excitable media. This mechanism may be operating in the mammalian pancreas, where excitable beta cells, quiescent when isolated, are found to oscillate when coupled, despite t...