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arXiv · 1903.02518

Stability and steady state of complex cooperative systems: a diakoptic approach

Philip Greulich·Benjamin D. MacArthur·Cristina Parigini·Rubén J. Sánchez García
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Abstract

Cooperative dynamics are common in ecology and population dynamics. However, their commonly high degree of complexity with a large number of coupled degrees of freedom renders them difficult to analyse. Here we present a graph-theoretical criterion, via a diakoptic approach (`divide-and-conquer') to determine a cooperative system's stability by decomposing the system's dependence graph into its strongly connected components (SCCs). In particular, we show that a linear cooperative system is Lyapunov stable if the SCCs of the associated dependence graph all have non-positive dominant eigenvalues, and if no SCCs which have dominant eigenvalue zero are connected by a path.

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Philip Greulich, Benjamin D. MacArthur, Cristina Parigini, Rubén J. Sánchez García. 2019-03-06. Stability and steady state of complex cooperative systems: a diakoptic approach. https://doi.org/10.1098/rsos.191090

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