Journal
ROYAL SOCIETY OPEN SCIENCE
Volume 6, Issue 12, Pages -Publisher
ROYAL SOC
DOI: 10.1098/rsos.191090
Keywords
cooperative systems; stability analysis; diakoptics; linear systems; population dynamics
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Funding
- Medical Research Council New Investigator Research [MR/R026610/1]
- Institute of Life Sciences
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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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