2026-06-26T08:38:32Zhttps://docta.ucm.es/rest/oai/requestoai:docta.ucm.es:20.500.14352/420022023-08-27T01:08:54Zcom_20.500.14352_14col_20.500.14352_15
Docta Complutense
author
Arrieta Algarra, José María
author
Cónsul, Neus
author
Oliva, Sergio M.
2023-06-20T00:06:54Z
2023-06-20T00:06:54Z
2010
0022-247X
10.1016/j.jmaa.2009.09.018
https://hdl.handle.net/20.500.14352/42002
http://www.sciencedirect.com/science/journal/0022247X
We consider a 1-dimensional reaction–diffusion equation with nonlinear boundary conditions of logistic type with delay. We deal with non-negative solutions and analyze the stability behavior of its unique positive equilibrium solution, which is given by the constant function u≡1. We show that if the delay is small, this equilibrium solution is asymptotically stable, similar as in the case without delay. We also show that, as the delay goes to infinity, this equilibrium becomes unstable and undergoes a cascade of Hopf bifurcations. The structure of this cascade will depend on the parameters appearing in the equation. This equation shows some dynamical behavior that differs from the case where the nonlinearity with delay is in the interior of the domain.
eng
Cascades of Hopf bifurcations from boundary delay
journal article
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599c8ae6ff3a1429967e30174bda7521
300207
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2009cascades-9.pdf
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65554
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2009cascades-9.pdf.txt