Diffusively coupled Lotka–Volterra system stabilized by heterogeneous graphs

Takashi Nagatani

Physica A: Statistical Mechanics and its Applications, 2019, vol. 525, issue C, 1114-1123

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.

Keywords: Networks; Lotka–Volterra model; Random walk; Stability; Stable focus; Metapopulation (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437119303590
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:525:y:2019:i:c:p:1114-1123

DOI: 10.1016/j.physa.2019.03.124

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().