Traveling waves of infinitely many pulses in nerve equations
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Cited by (14)
Evans functions and bifurcations of nonlinear waves of some nonlinear reaction diffusion equations
2017, Journal of Differential EquationsCitation Excerpt :The same results about the standing pulse solution and the standing wave fronts hold for the nonlinear scalar reaction diffusion equation (4) as for equation (3), under the corresponding conditions. For the existence, stability and instability of the nonlinear waves (the traveling wave front, the traveling wave back, the standing pulse solutions and the standing wave fronts) of the nonlinear system of reaction diffusion equations and the nonlinear scalar reaction diffusion equations, there have been some very interesting results by using ideas and methods other than Evans functions, see [7–9,15–20,23–27]. There have been many other related very interesting results in reaction diffusion equations.
Traveling waves in the Baer and Rinzel model of spine studded dendritic tissue
2002, Physica D: Nonlinear PhenomenaCitation Excerpt :The spatially extended FitzHugh–Nagumo equations with a piece-wise linear non-linearity is one such example (where one can guarantee complex eigenvalues) and admits to mathematical analysis. For this model it has been possible to extend results due to Šilnikov and show the existence of an uncountable discrete family of traveling waves which are trains of infinitely many pulses [22]. Periodic and solitary waves in this model have also been extensively analyzed by Rinzel and Keller [23].
Elements of Applied Bifurcation Theory: Fourth Edition
2023, Applied Mathematical Sciences (Switzerland)Evans functions and bifurcations of standing wave fronts of a nonlinear system of reaction diffusion equations
2016, Journal of Applied Analysis and ComputationMultiple time scale dynamics
2015, Applied Mathematical Sciences (Switzerland)