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

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 dynam-
ics 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 deter-
mine 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 sta-
ble if the SCCs of the associated dependence graph all have non-
positive dominant eigenvalues, and if any two SCCs which have dom-
inant eigenvalue zero are not connected by any path.
Greulich, Philip
65da32ad-a73a-435a-86e0-e171437430a9
Macarthur, Benjamin
2c0476e7-5d3e-4064-81bb-104e8e88bb6b
Sanchez Garcia, Ruben
8246cea2-ae1c-44f2-94e9-bacc9371c3ed
Parigini, Cristina
e703096b-49c9-43e6-af7c-62a3a85e9a9b
Greulich, Philip
65da32ad-a73a-435a-86e0-e171437430a9
Macarthur, Benjamin
2c0476e7-5d3e-4064-81bb-104e8e88bb6b
Sanchez Garcia, Ruben
8246cea2-ae1c-44f2-94e9-bacc9371c3ed
Parigini, Cristina
e703096b-49c9-43e6-af7c-62a3a85e9a9b

Greulich, Philip, Macarthur, Benjamin, Sanchez Garcia, Ruben and Parigini, Cristina (2019) Stability and steady state of complex cooperative systems: a diakoptic approach. Pre-print.

Record type: Article

Abstract

Cooperative dynamics are common in ecology, population dynam-
ics 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 deter-
mine 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 sta-
ble if the SCCs of the associated dependence graph all have non-
positive dominant eigenvalues, and if any two SCCs which have dom-
inant eigenvalue zero are not connected by any path.

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stab-coop-sys_arxiv1903.02518 - Author's Original
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e-pub ahead of print date: 6 March 2019

Identifiers

Local EPrints ID: 429384
URI: https://eprints.soton.ac.uk/id/eprint/429384
PURE UUID: b5b24ffe-ed70-4c79-a744-ab29707e757d
ORCID for Philip Greulich: ORCID iD orcid.org/0000-0001-5247-6738
ORCID for Ruben Sanchez Garcia: ORCID iD orcid.org/0000-0001-6479-3028

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Date deposited: 27 Mar 2019 17:30
Last modified: 28 Mar 2019 01:32

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