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Journal articles

Bifurcations and Synchronization in Networks of Unstable Reaction–Diffusion Systems

Abstract : 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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https://hal.archives-ouvertes.fr/hal-03189543
Contributor : Guillaume CANTIN Connect in order to contact the contributor
Submitted on : Sunday, April 4, 2021 - 9:19:03 AM
Last modification on : Friday, May 20, 2022 - 3:36:51 AM

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

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