Abstract
In this work we study a reaction–diffusion problem with delay and we make an analysis of the stability of solutions by means of bifurcation theory. We take the delay constant as a parameter. Special conditions on the vector field assure existence of a spatially nonconstant positive equilibrium Uk , which is stable for small values of the delay. An increase of the delay destabilizes the equilibrium of Uk and leads to super or subcritical Hopf bifurcation.
Dedicated to Professor José Geraldo Dos Reis.
E-mail: [email protected]
Acknowledgments
We appreciate the generous comments of Professor A.N. Carvalho which greatly improved the readability of the article. Santos was supported by FAPESP, grant # 97/11717-4.
Notes
Dedicated to Professor José Geraldo Dos Reis.
E-mail: [email protected]