Stability and steady state of complex cooperative systems: a diakoptic approach
| Autor: | Rubén J. Sánchez-García, Cristina Parigini, Ben D. MacArthur, Philip Greulich |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Lyapunov function
Strongly connected component Population 010103 numerical & computational mathematics Dynamical Systems (math.DS) Topology stability analysis 01 natural sciences 03 medical and health sciences symbols.namesake cooperative systems Diakoptics FOS: Mathematics population dynamics 0101 mathematics Mathematics - Dynamical Systems education lcsh:Science Eigenvalues and eigenvectors 030304 developmental biology Mathematics 0303 health sciences education.field_of_study Multidisciplinary Linear system linear systems diakoptics symbols Graph (abstract data type) lcsh:Q Research Article |
| Zdroj: | Royal Society Open Science, Vol 6, Iss 12 (2019) Royal Society Open Science |
| Popis: | 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. 18 pages, 2 figures. Major changes (introduction and conclusions rewritten, new proof of Theorem 2) |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|