Transient wave forms in neural networks with diffusive and nonlocal coupling have attracted particular interest because they may mediate recruitment of healthy cortical tissue into a pathological state during migraine. To investigate this process, we use a reaction-diffusion system of inhibitor-activator type as a generic model of pathological wave propagation and set it close to bifurcation in...

This paper investigates traveling wave solutions of the spatially discrete reaction-diffusion systems whose kinetics are modeled by the McKean caricature of the FitzHugh-Nagumo model. In the limit of a weak coupling strength, we construct the traveling wave solutions and obtain the critical coupling constant below which propagation failure occurs. We report the existence of two different pulse ...

A formulism of frequency-domainmass diffusion-waves in porousmedia is derived bymeans of Fourier transform. In analogy to conventional thermal-wave fields, internally consistent Green functions inCartesian coordinates for linearmass diffusion-waves is also presented for infinite, semiinfinite andfinite-size domains in three-dimensional spaces. TheGreen functions are utilized to analyze the resp...

One of the main characteristics of blood coagulation is the speed of clot growth. In the current work we consider a mathematical model of the coagulation cascade and study existence, stability and speed of propagation of the reaction-diffusion waves of blood coagulation. We also develop a simplified one-equation model that reflects the main features of the thrombin wave propagation. For this eq...

The problem of propagation of plane wave including body and surface waves propagating in a transversely isotropic half-space with a depth-wise axis of material symmetry is investigated in details. Using the advantage of representation of displacement fields in terms of two complete scalar potential functions, the coupled equations of motion are uncoupled and reduced to two independent equations...

Under certain conditions, cardiac myocytes engage in a mode of calcium signaling in which calcium release from the sarcoplasmic reticulum (SR) to myoplasm occurs in self-propagating succession along the length of the cell. This event is called a calcium wave and is fundamentally a diffusion-reaction phenomenon. We present a simple, continuum mathematical model that simulates calcium waves. The ...

Many models in biology and ecology can be described by reaction-diffusion equations wit time delay. One of important solutions for these type of equations is the traveling wave solution that shows the phenomenon of wave propagation. The existence of traveling wave fronts has been proved for large class of equations, in particular, the monotone systems, such as the cooperative systems and some c...

In this paper, on the basis of a new strain gradient elasticity theory, wave propagation in rectangular nanoplates by considering in-plane magnetic field is studied. This strain gradient theory has two gradient parameters and has the ability to compare with the nonlocal elasticity theory. From the best knowledge of author, it is the first time that this theory is used for investigating wave pro...

The present investigation deals with the propagation of waves in a micropolar transversely isotropic layer. Secular equations for symmetric and skew-symmetric modes of wave propagation in completely separate terms are derived. The amplitudes of displacements and microrotation were also obtained. Finally, the numerical solution was carried out for aluminium epoxy material and the dispersion curv...