RT Journal Article
T1 Cascades of Hopf bifurcations from boundary delay
A1 Arrieta Algarra, José María
A1 Cónsul, Neus
A1 Oliva, Sergio M.
AB 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.
PB Elsevier
SN 0022-247X
YR 2010
FD 2010
LK https://hdl.handle.net/20.500.14352/42002
UL https://hdl.handle.net/20.500.14352/42002
LA eng
NO MEC
NO SIMUMAT-Comunidad de Madrid
NO Ministerio de Educación y Ciencia
NO FAPESP
NO CAPES
NO Programa de Financiación de Grupos de Investigación UCM-Comunidad de Madrid CCG07- UCM/ESP-2393. Grupo 920894.
DS Docta Complutense
RD 2 may 2024