Article
Bifurcation from zero of a complete trajectory for non-autonomous logistic PDEs
Author/s | Langa Rosado, José Antonio
Robinson, James C. Suárez Fernández, Antonio |
Department | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Publication Date | 2005-08 |
Deposit Date | 2016-07-06 |
Published in |
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Abstract | 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 ... 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. |
Funding agencies | Ministerio de Educación y Ciencia (MEC). España European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER) |
Project ID. | BFM2002- 03068
BFM2003-06446 |
Citation | 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. |
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