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We study the problem of initiation of excitation waves in the FitzHugh-Nagumo model. Our approach follows earlier works and is based on the idea of approximating the boundary between basins of attraction of propagating waves and of the…

We consider the problem of initiation of a propagating wave in a one-dimensional excitable fibre. In the Zeldovich-Frank-Kamenetsky equation, a.k.a. Nagumo equation, the key role is played by the "critical nucleus'' solution whose stable…

Linearization around unstable travelling waves in excitable systems can be used to approximate strength-extent curves in the problem of initiation of excitation waves for a family of spatially confined perturbations to the rest state. This…

This paper considers particle propagation in a cylindrical molecular communication channel, e.g. a simplified model of a blood vessel. Emitted particles are influenced by diffusion, flow, and a vertical force induced e.g. by gravity or…

In order to describe excitable reaction-diffusion systems, we derive a two-dimensional model with a Hopf and a semilocal saddle-node homoclinic bifurcation. This model gives the theoretical framework for the analysis of the saddle-node…

We consider the strength-duration relationship in one-dimensional spatially extended excitable media. In a previous study [Idris and Biktashev 2008] set out to separate initial (or boundary) conditions leading to propagation wave solutions…

In this paper, we present an enhanced semi-analytic method for calculating quasinormal excitation factors in the eikonal regime, specifically for Schwarzschild black holes. To achieve improved accuracy in our quasinormal mode computations,…

Wave motion in two- and three-dimensional periodic lattices of beam members supporting longitudinal and flexural waves is considered. An analytic method for solving the Bloch wave spectrum is developed, characterized by a generalized…

A unified electrodynamic approach to the guided-wave excitation theory is generalized to the waveguiding structures containing a hypothetical space-dispersive medium with drifting charge carriers possessing simultaneously elastic,…

Detailed ionic models of cardiac cells are difficult for numerical simulations because they consist of a large number of equations and contain small parameters. The presence of small parameters, however, may be used for asymptotic reduction…

Wave propagation in one-dimensional heterogeneous bistable media is studied using the Schl\"ogl model as a representative example. Starting from the analytically known traveling wave solution for the homogeneous medium, infinitely extended,…

We focus on the (sharp) threshold phenomena arising in some reaction-diffusion equations supplemented with some compactly supported initial data. In the so-called ignition and bistable cases, we prove the first sharp quantitative estimate…

Excitable media are systems which are at rest in the absence of external input but which respond to a sufficiently strong stimulus by sending a wave of "excitation" across the medium. Examples include cardiac and cortical tissue, and in…

The scattering of electromagnetic waves by an obstacle is analyzed through a set of partial differential equations combining the Maxwell's model with the mechanics of fluids. Solitary type EM waves, having compact support, may easily be…

We analyze the effects of spatially extended periodic forcing on the dynamics of one-dimensional excitation waves. Entrainment of unstable primary waves has been studied numerically for different amplitudes and frequencies of additional…

Wave propagation in a stratified fluid / porous medium is studied here using analytical and numerical methods. The semi-analytical method is based on an exact stiffness matrix method coupled with a matrix conditioning procedure, preventing…

In a previous work the authors described a fast high-fidelity computer model for acoustic scattering from multi-layered elastic spheres. This work is now extended with a scaling strategy significantly mitigating the problem of overflow and…

In this work, we are interested in solving large linear systems stemming from the Extra-Membrane-Intra (EMI) model, which is employed for simulating excitable tissues at a cellular scale. After setting the related systems of partial…

We consider the problem of initiation of propagating wave in a one-dimensional excitable fiber. In the FitzHugh-Nagumo theory, the key role is played by ``critical nucleus'' and ``critical pulse'' solutions whose (center-)stable manifold is…

The wave equation with energy critical sources and nonlinear damping defined on a 3D bounded domain is considered. It is shown that the resulting dynamical system admits a global attractor. Under the additional assumption of strong…