Stability and steady state of complex cooperative systems: a diakoptic approach
11 Jun 2020
•
Greulich Philip
•
MacArthur Benjamin D.
•
Parigini Cristina
•
García Rubén J. Sánchez
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.(read more)