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


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.

SUBMITTER: Greulich P 

PROVIDER: S-EPMC6936286 | biostudies-literature | 2019 Dec

REPOSITORIES: biostudies-literature

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

Greulich Philip P   MacArthur Ben D BD   Parigini Cristina C   Sánchez-García Rubén J RJ  

Royal Society open science 20191204 12


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 Lyapun  ...[more]

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