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In this work, we propose and study the stability of nerve impulse propagation as electrical and mechanical signals through linear approximation. We present a potential energy stored in the biomembrane due to the deformation, bending, and stretching as the action potential propagates in the nerve fibre. From the potential energy, we derive electromechanical coupling forces and an attempt is made to unify the two models to account for both the electrical and mechanical activities of nerve signal propagation by introducing the electromechanical coupling forces. We examine the stability of the equilibrium states of the electromechanical model for nerves through the Routh Hurwitz stability criteria. Finally, we present results of the numerical simulations of the electromechanical model for nerves through Runge Kutta method of order four.
In this work, we consider the electromechanical density pulse as a coupled solitary waves represented by a longitudinal compression wave and an out-of-plane transversal wave (i.e., perpendicular to the membrane surface). We analyzed using, the variat
Localized spot patterns, where one or more solution components concentrates at certain points in the domain, are a common class of localized pattern for reaction-diffusion systems, and they arise in a wide range of modeling scenarios. In an arbitrary
We present a stability analysis of the Lugiato-Lefever model for Kerr optical frequency combs in whispering gallery mode resonators pumped in the anomalous dispersion regime. This article is the second part of a research work whose first part was dev
We consider a bulk-membrane-coupled partial differential equation in which a single diffusion equation posed within the unit ball is coupled to a two-component reaction diffusion equation posed on the bounding unit sphere through a linear Robin bound
A dynamical theory of geophysical precipitation pattern formation is presented and applied to irreversible calcium carbonate (travertine) deposition. Specific systems studied here are the terraces and domes observed at geothermal hot springs, such as