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Dimension estimate of attractors for complex networks of reaction-diffusion systems applied to an ecological model

Abstract : The asymptotic behavior of dissipative evolution problems, determined by complex networks of reaction-diffusion systems, is investigated with an original approach. We establish a novel estimation of the fractal dimension of exponential attractors for a wide class of continuous dynamical systems, clarifying the effect of the topology of the network on the large time dynamics of the generated semi-flow. We explore various remarkable topologies (chains, cycles, star and complete graphs) and discover that the size of the network does not necessarily enlarge the dimension of attractors. Additionally, we prove a synchronization theorem in the case of symmetric topologies. We apply our method to a complex network of competing species systems modeling an heterogeneous biological ecosystem and propose a series of numerical simulations which underpin our theoretical statements.
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https://hal.archives-ouvertes.fr/hal-03175738
Contributor : Guillaume CANTIN Connect in order to contact the contributor
Submitted on : Sunday, March 21, 2021 - 8:58:25 AM
Last modification on : Thursday, May 19, 2022 - 3:11:55 PM

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Guillaume Cantin, M. A. Aziz-Alaoui. Dimension estimate of attractors for complex networks of reaction-diffusion systems applied to an ecological model. Communications on Pure & Applied Analysis, American Institute of Mathematical Sciences (AIMS) 2021, 20 (2), pp.623-650. ⟨10.3934/cpaa.2020283⟩. ⟨hal-03175738⟩

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