Arrieta Algarra, José María y Cónsul, Neus y Oliva, Sergio M. (2010) Cascades of Hopf bifurcations from boundary delay. Journal of Mathematical Analysis and Applications , 361 (1). pp. 19-37. ISSN 0022-247X
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.
|Tipo de documento:||Artículo|
|Palabras clave:||Logistic equation; Periodic orbits; One space dimension; Nonlinear boundary conditions|
|Materias:||Ciencias > Matemáticas > Ecuaciones diferenciales|
|Depositado:||18 Nov 2011 08:32|
|Última Modificación:||06 Feb 2014 09:55|
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