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Comparison and convergence to equilibrium in a nonlocal delayed reaction-diffusion model on an infinite domain
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posted on 2023-06-08, 08:44 authored by Michele V Bartuccelli, S A Gourley, Yuliya KyrychkoYuliya KyrychkoWe study a nonlocal time-delayed reaction-di®usion population model on an in¯nite one-dimensional spatial domain. Depending on the model parameters, a non-trivial uniform equilibrium state may exist. We prove a comparison theorem for our equation for the case when the birth function is monotone, and then we use this to establish nonlinear stability of the non-trivial uniform equilibrium state when it exists. A certain class of non-monotone birth functions relevant to certain species is also considered, namely birth functions that are increasing at low densities but decreasing at high densities. In this case we prove that solutions still converge to the non-trivial equilibrium, provided the birth function is increasing at the equilibrium level.
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Publication status
- Published
Journal
Discrete and Continuous Dynamical Systems - Series BISSN
1531-3492Publisher
American Institute of Mathematical SciencesIssue
4Volume
5Page range
1015-1026Department affiliated with
- Mathematics Publications
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- No
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- Yes
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2012-02-06Usage metrics
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