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Partitioning a reaction-diffusion ecological network for dynamic stability

Kumar, Dinesh and Gupta, Jatin and Raha, Soumyendu (2019) Partitioning a reaction-diffusion ecological network for dynamic stability. In: PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 475 (2223).

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Official URL: https://doi.org/10.1098/rspa.2018.0524

Abstract

The loss of dispersal connections between habitat patches may destabilize populations in a patched ecological network. This work studies the stability of populations when one or more communication links is removed. An example is finding the alignment of a highway through a patched forest containing a network of metapopulations in the patches. This problem is modelled as that of finding a stable cut of the graph induced by the metapopulations network, where nodes represent the habitat patches and the weighted edges model the dispersal between habitat patches. A reaction-diffusion system on the graph models the dynamics of the predator-prey system over the patched ecological network. The graph Laplacian's Fiedler value, which indicates the well-connectedness of the graph, is shown to affect the stability of the metapopulations. We show that, when the Fiedler value is sufficiently large, the removal of edges without destabilizing the dynamics of the network is possible. We give an exhaustive graph partitioning procedure, which is suitable for smaller networks and uses the criterion for both the local and global stability of populations in partitioned networks. A heuristic graph bisection algorithm that preserves the preassigned lower bound for the Fiedler value is proposed for larger networks and is illustrated with examples.

Item Type: Journal Article
Additional Information: Copyright of this article belongs to ROYAL SOC
Keywords: ecological networks; dynamical system stability; graph partitioning
Department/Centre: Division of Interdisciplinary Research > Computational and Data Sciences
Depositing User: LIS Interns
Date Deposited: 27 May 2019 06:15
Last Modified: 27 May 2019 06:15
URI: http://eprints.iisc.ac.in/id/eprint/62741

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