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Chaos and crises in a model for cooperative hunting: A symbolic dynamics approach

2009-12Journal article Open access
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dc.contributor.authorDuarte, Jorge
dc.contributor.authorJanuário, Cristina
dc.contributor.authorMartins, Nuno
dc.contributor.authorSardanyes, Josep
dc.date.accessioned2012-03-13T16:47:33Z
dc.date.available2012-03-13T16:47:33Z
dc.date.issued2009-12
dc.description.abstractIn this work we investigate the population dynamics of cooperative hunting extending the McCann and Yodzis model for a three-species food chain system with a predator, a prey, and a resource species. The new model considers that a given fraction sigma of predators cooperates in prey's hunting, while the rest of the population 1-sigma hunts without cooperation. We use the theory of symbolic dynamics to study the topological entropy and the parameter space ordering of the kneading sequences associated with one-dimensional maps that reproduce significant aspects of the dynamics of the species under several degrees of cooperative hunting. Our model also allows us to investigate the so-called deterministic extinction via chaotic crisis and transient chaos in the framework of cooperative hunting. The symbolic sequences allow us to identify a critical boundary in the parameter spaces (K, C-0) and (K, sigma) which separates two scenarios: (i) all-species coexistence and (ii) predator's extinction via chaotic crisis. We show that the crisis value of the carrying capacity K-c decreases at increasing sigma, indicating that predator's populations with high degree of cooperative hunting are more sensitive to the chaotic crises. We also show that the control method of Dhamala and Lai [Phys. Rev. E 59, 1646 (1999)] can sustain the chaotic behavior after the crisis for systems with cooperative hunting. We finally analyze and quantify the inner structure of the target regions obtained with this control method for wider parameter values beyond the crisis, showing a power law dependence of the extinction transients on such critical parameters.por
dc.identifier.citationDuarte J, Januário C, Martins N, Martins N, Sardanyes J.Chaos and crises in a model for cooperative hunting: A symbolic dynamics approach. Chaos,. 2009; 19 (4): Art. No. 043102.por
dc.identifier.issn1054-1500
dc.identifier.urihttp://hdl.handle.net/10400.21/1281
dc.language.isoengpor
dc.peerreviewedyespor
dc.publisherAmer Inst Physicspor
dc.relation.ispartofseries4;043102
dc.subjectControlling Transient Chaospor
dc.subjectFood-Chainpor
dc.subjectPredatorpor
dc.subjectAttractorspor
dc.titleChaos and crises in a model for cooperative hunting: A symbolic dynamics approachpor
dc.typejournal article
dspace.entity.typePublication
oaire.citation.conferencePlaceMelvillepor
oaire.citation.issue19por
oaire.citation.titleChaospor
person.familyNameDuarte
person.familyNameJanuário
person.givenNameJorge
person.givenNameCristina
person.identifier.ciencia-idBC1D-1E83-E2B2
person.identifier.orcid0000-0003-2641-3199
person.identifier.orcid0000-0002-6978-876X
person.identifier.ridG-7261-2011
person.identifier.scopus-author-id35310049800
person.identifier.scopus-author-id56526791400
rcaap.rightsrestrictedAccesspor
rcaap.typearticlepor
relation.isAuthorOfPublication4dbec82a-caa4-4662-b156-af73687e867f
relation.isAuthorOfPublication42a4023b-b4c4-4456-aaba-d97bf8c14d6a
relation.isAuthorOfPublication.latestForDiscovery42a4023b-b4c4-4456-aaba-d97bf8c14d6a

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