A mean-field method using local Fokker-Planck equations computes stationary states and maps phase diagrams for Lotka-Volterra dynamics on sparse asymmetric graphs.
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A minimal neighbor-interaction Lotka-Volterra model yields exponentially many self-organized species cluster states separated by sharp phase transitions, exactly solvable via transfer matrices in the nearest-neighbor limit.
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Local equations for the generalized Lotka-Volterra model on sparse asymmetric graphs
A mean-field method using local Fokker-Planck equations computes stationary states and maps phase diagrams for Lotka-Volterra dynamics on sparse asymmetric graphs.
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Minimal model of self-organized clusters with phase transitions in ecological communities
A minimal neighbor-interaction Lotka-Volterra model yields exponentially many self-organized species cluster states separated by sharp phase transitions, exactly solvable via transfer matrices in the nearest-neighbor limit.