Article Dans Une Revue Journal of Nonlinear Science Année : 2021

Bifurcations and Synchronization in Networks of Unstable Reaction–Diffusion Systems

Résumé

This article is devoted to the analysis of the dynamics of a complex network of unstable reaction–diffusion systems. We demonstrate the existence of a non-empty parameter regime for which synchronization occurs in non-trivial attractors. We establish a lower bound of the dimension of the global attractor in an innovative manner, by proving a novel theorem of continuity of the unstable manifold, for which we invoke a principle of spectrum perturbation of non-bounded operators. Finally, we exhibit a co-dimension 2 bifurcation of the unstable manifold which shows that synchronization is compatible with instabilities.

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Dates et versions

hal-03189543 , version 1 (04-04-2021)

Identifiants

Citer

Alain Miranville, Guillaume Cantin, M. Aziz-Alaoui. Bifurcations and Synchronization in Networks of Unstable Reaction–Diffusion Systems. Journal of Nonlinear Science, 2021, 31 (2), ⟨10.1007/s00332-021-09701-9⟩. ⟨hal-03189543⟩
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