Metapopulations is a multi-patch habitat system, where populations live and interact in  habitat patches, and individuals disperse from one patch to  other via dispersal connections. The loss of dispersal connections among  habitat patches can impact negatively on the stability of the system. This paper aims to determine some necessary and sufficient mathematical conditions for an appropriate metapopulations network partitioning (spatial cut) such that populations remain linearly stable in the partitioninginduced daughter subnetworks. For that, metapopulations stability analysed and role of the Fiedler value of a metapopulations induced graph Laplacian described first . Our study suggests, sufficiently connected metapopulations network (having the Fiedler value greater than or equal to some threshold level) along with the constrained internal patch dynamicsalways results in stable metapopulations dynamics around its co-existential equilibrium solution .
A metapopulations network is a multi-patch habitat system, where populations live and interact in the habitat patches, and individuals disperse from one patch to the other via dispersal connections. The loss of dispersal connections among the habitat patches can impact the stability of the system. In this work, we determine if there exist(s) set(s) of dispersal connections removal of which causes partitioning(s) of the metapopulations network into dynamically stable sub-networks . Our study finds that there exists a lower bound threshold Fiedler value which guarantees the dynamical stability of the network dynamics. Necessary and sufficient mathematical conditions for finding partitions that result in sub-networks with the desired threshold Fiedler values have been derived and illustrated with examples. Although posed and discussed in the ecological context, it may be pointed out that such partitioning problems exist across any spatially discrete but connected dynamical systems with reaction-diffusion. Non-ecological examples are power distribution grids, intra-cellular reaction pathway networks and high density nano-fluidic lab-on-chip applications .
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This paper aims to determine some necessary and sufficient mathematical conditions for an appropriate metapopulations network partitioning (spatial cut) such that populations remain linearly stable in the partitioninginduced daughter subnetworks. For that, metapopulations stability analysed and role of the Fiedler value of a metapopulations induced graph Laplacian described first
In this work, we determine if there exist(s) set(s) of dispersal connections removal of which causes partitioning(s) of the metapopulations network into dynamically stable sub-networks
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suggests, sufficiently connected metapopulations network (having the Fiedler value greater than or equal to some threshold level) along with the constrained internal patch dynamicsalways results in stable metapopulations dynamics around its co-existential equilibrium solution
finds that there exists a lower bound threshold Fiedler value which guarantees the dynamical stability of the network dynamics. Necessary and sufficient mathematical conditions for finding partitions that result in sub-networks with the desired threshold Fiedler values have been derived and illustrated with examples. Although posed and discussed in the ecological context, it may be pointed out that such partitioning problems exist across any spatially discrete but connected dynamical systems with reaction-diffusion. Non-ecological examples are power distribution grids, intra-cellular reaction pathway networks and high density nano-fluidic lab-on-chip applications