DIMENSION ESTIMATE OF ATTRACTORS FOR COMPLEX NETWORKS OF REACTION-DIFFUSION SYSTEMS APPLIED TO AN ECOLOGICAL MODEL

被引:2
作者
Cantin, Guillaume [1 ]
Aziz-Alaoui, M. A. [1 ]
机构
[1] Normandie Univ, Lab Math Appl Havre, FR CNRS 3335, ISCN, F-76600 Le Havre, France
关键词
Dynamical system; reaction-diffusion; complex network; exponential attractor; fractal dimension; synchronization; competing species; EQUATIONS; COMPETITION;
D O I
10.3934/cpaa.2020283
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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.
引用
收藏
页码:623 / 650
页数:28
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