Stability and steady state of complex cooperative systems: a diakoptic approach.
R Soc Open Sci
; 6(12): 191090, 2019 Dec.
Article
en En
| MEDLINE
| ID: mdl-31903203
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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1
Colección:
01-internacional
Banco de datos:
MEDLINE
Idioma:
En
Revista:
R Soc Open Sci
Año:
2019
Tipo del documento:
Article
País de afiliación:
Reino Unido