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Diffusively coupled Lotka–Volterra system stabilized by heterogeneous graphs

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  • Nagatani, Takashi

Abstract

We study the effect of the network structure on the dynamic stability in the diffusively coupled Lotka–Volterra system. Here we present a metapopulation model for the Lotka–Volterra system on various graphs. The total population is assumed to consist of several subpopulations (nodes). Each individual migrates by random walk; the destination of migration is randomly determined. From reaction–diffusion equations, we obtain the population dynamics. The numerical analyses are performed only for a few and characteristic values of the parameters representing typical behaviors. It is found that the dynamics highly depends on network structures. When a network is homogeneous, the dynamics are neutrally stable: each node has a periodic solution with neutral stability, and the oscillations synchronize in all nodes. However, when a network is heterogeneous, the dynamics approach stable focus and all nodes reach equilibriums with different densities. Hence, the heterogeneity of the network induces dynamic stabilization.

Suggested Citation

  • Nagatani, Takashi, 2019. "Diffusively coupled Lotka–Volterra system stabilized by heterogeneous graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 1114-1123.
    • Handle: RePEc:eee:phsmap:v:525:y:2019:i:c:p:1114-1123
    DOI: 10.1016/j.physa.2019.03.124
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    Cited by:

    1. Bazeia, D. & de Oliveira, B.F. & Silva, J.V.O. & Szolnoki, A., 2020. "Breaking unidirectional invasions jeopardizes biodiversity in spatial May-Leonard systems," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    2. Szolnoki, Attila & Chen, Xiaojie, 2020. "Strategy dependent learning activity in cyclic dominant systems," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).

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