scholarly journals Nonlinear Stability of Traveling Waves in a Monostable Epidemic Model with Delay

2017 ◽  
Vol 21 (6) ◽  
pp. 1381-1411
Author(s):  
Xin Wu ◽  
Zhaohai Ma ◽  
Rong Yuan
Keyword(s):  
Nonlinear Stability ◽  
Traveling Waves ◽  
Epidemic Model

Nonlinear stability of traveling waves for a multi-type SIS epidemic model

2018 ◽  
Vol 11 (01) ◽  
pp. 1850003
Author(s):  
Mengqi Li ◽  
Peixuan Weng ◽  
Yong Yang
Keyword(s):  
Nonlinear Stability ◽  
Traveling Waves ◽  
Epidemic Model ◽  
Wave Speed ◽  
Initial Perturbation ◽  
Large Wave ◽  
Weighted Energy ◽  
Sis Epidemic Model ◽  
Traveling Wavefront ◽  
Sis Epidemic

The nonlinear stability of traveling waves for a multi-type SIS epidemic model is investigated in this paper. By using the comparison principle together with the weighted energy function, we obtain the exponential stability of traveling wavefront with large wave speed. The initial perturbation around the traveling wavefront decays exponentially as [Formula: see text], but it can be arbitrarily large in other locations.

scholarly journals Hyperbolic traveling waves driven by growth

2014 ◽  
Vol 24 (06) ◽  
pp. 1165-1195 ◽  
Author(s):  
Emeric Bouin ◽  
Vincent Calvez ◽  
Grégoire Nadin
Keyword(s):  
Nonlinear Stability ◽  
Traveling Waves ◽  
Hyperbolic Model ◽  
Kpp Equation ◽  
Transition Parameter ◽  
Minimal Speed ◽  
Traveling Fronts ◽  
Traveling Front ◽  
Maximal Speed ◽  
Existence And Stability

We perform the analysis of a hyperbolic model which is the analog of the Fisher-KPP equation. This model accounts for particles that move at maximal speed ϵ-1 (ϵ > 0), and proliferate according to a reaction term of monostable type. We study the existence and stability of traveling fronts. We exhibit a transition depending on the parameter ϵ: for small ϵ the behavior is essentially the same as for the diffusive Fisher-KPP equation. However, for large ϵ the traveling front with minimal speed is discontinuous and travels at the maximal speed ϵ-1. The traveling fronts with minimal speed are linearly stable in weighted L2 spaces. We also prove local nonlinear stability of the traveling front with minimal speed when ϵ is smaller than the transition parameter.

EVANS FUNCTIONS AND NONLINEAR STABILITY OF TRAVELING WAVES IN NEURONAL NETWORK MODELS

2007 ◽  
Vol 17 (08) ◽  
pp. 2693-2704 ◽  
Author(s):  
BJÖRN SANDSTEDE
Keyword(s):  
Differential Equations ◽  
Neuronal Network ◽  
Nonlinear Stability ◽  
Traveling Waves ◽  
Network Models ◽  
Function Spaces ◽  
Spectral Stability ◽  
Evans Function ◽  
Evans Functions

Modeling networks of synaptically coupled neurons often leads to systems of integro-differential equations. Particularly interesting solutions in this context are traveling waves. We prove here that spectral stability of traveling waves implies their nonlinear stability in appropriate function spaces, and compare several recent Evans-function constructions that are useful tools when analyzing spectral stability.

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