Stability and steady state of complex cooperative systems: a diakoptic approach
Stability and steady state of complex cooperative systems: a diakoptic approach
Cooperative dynamics are common in ecology, population dynamics and in generalised compartment models. However, their commonly high degree of complexity with a large number of coupled degrees of freedom makes them difficult to analyse. Here we present a graphical criterion, via a diakoptic approach ("divide-and-conquer") to determine a cooperative system's stability by decomposing the system's interaction 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 any two SCCs which have dominant eigenvalue zero are not connected by any path.
1-9
Greulich, Philip
65da32ad-a73a-435a-86e0-e171437430a9
Macarthur, Benjamin
2c0476e7-5d3e-4064-81bb-104e8e88bb6b
Parigini, Cristina
e703096b-49c9-43e6-af7c-62a3a85e9a9b
Sanchez Garcia, Ruben
8246cea2-ae1c-44f2-94e9-bacc9371c3ed
December 2019
Greulich, Philip
65da32ad-a73a-435a-86e0-e171437430a9
Macarthur, Benjamin
2c0476e7-5d3e-4064-81bb-104e8e88bb6b
Parigini, Cristina
e703096b-49c9-43e6-af7c-62a3a85e9a9b
Sanchez Garcia, Ruben
8246cea2-ae1c-44f2-94e9-bacc9371c3ed
Greulich, Philip, Macarthur, Benjamin, Parigini, Cristina and Sanchez Garcia, Ruben
(2019)
Stability and steady state of complex cooperative systems: a diakoptic approach.
Royal Society Open Science, 6 (12), .
(doi:10.1098/rsos.191090).
Abstract
Cooperative dynamics are common in ecology, population dynamics and in generalised compartment models. However, their commonly high degree of complexity with a large number of coupled degrees of freedom makes them difficult to analyse. Here we present a graphical criterion, via a diakoptic approach ("divide-and-conquer") to determine a cooperative system's stability by decomposing the system's interaction 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 any two SCCs which have dominant eigenvalue zero are not connected by any path.
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stab-coop-sys_arxiv1903.02518
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Stability of complex cooperative systems a diakoptic approach
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Accepted/In Press date: 22 November 2019
e-pub ahead of print date: 4 December 2019
Published date: December 2019
Additional Information:
manuscript submitted to Royal Society Open Science
Identifiers
Local EPrints ID: 429384
URI: http://eprints.soton.ac.uk/id/eprint/429384
ISSN: 2054-5703
PURE UUID: b5b24ffe-ed70-4c79-a744-ab29707e757d
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Date deposited: 27 Mar 2019 17:30
Last modified: 16 Mar 2024 04:17
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Author:
Cristina Parigini
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