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Bifurcation from zero of a complete trajectory for non-autonomous logistic PDEs

Opened Access Bifurcation from zero of a complete trajectory for non-autonomous logistic PDEs

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Autor: Langa Rosado, José Antonio
Robinson, James C.
Suárez Fernández, Antonio
Departamento: Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
Fecha: 2005-08
Publicado en: International Journal of Bifurcation and Chaos, 15 (8), 2663-2669.
Tipo de documento: Artículo
Resumen: In this paper we extend the well-known bifurcation theory for autonomous logistic equations to the non-autonomous equation ut − ∆u = λu − b(t)u 2 with b(t) ∈ [b0, B0], 0 < b0 < B0 < 2b0. In particular, we prove the existence of a unique uniformly bounded trajectory that bifurcates from zero as λ passes through the first eigenvalue of the Laplacian, which attracts all other trajectories. Although it is this relatively simple equation that we analyse in detail, other more involved models can be treated using similar techniques.
Cita: Langa Rosado, J.A., Robinson, J.C. y Suárez Fernández, A. (2005). Bifurcation from zero of a complete trajectory for non-autonomous logistic PDEs. International Journal of Bifurcation and Chaos, 15 (8), 2663-2669.
Tamaño: 185.4Kb
Formato: PDF

URI: http://hdl.handle.net/11441/43225

DOI: 10.1142/S0218127405013605

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