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Topological Complexity and Predictability in the Dynamics of a Tumor Growth Model with Shilnikov's Chaos

2013-07Journal article Open access
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dc.contributor.authorDuarte, Jorge
dc.contributor.authorJanuário, Cristina
dc.contributor.authorRodrigues, Carla
dc.contributor.authorSardanyes, Josep
dc.date.accessioned2013-11-02T19:55:33Z
dc.date.available2013-11-02T19:55:33Z
dc.date.issued2013-07
dc.description.abstractDynamical systems modeling tumor growth have been investigated to determine the dynamics between tumor and healthy cells. Recent theoretical investigations indicate that these interactions may lead to different dynamical outcomes, in particular to homoclinic chaos. In the present study, we analyze both topological and dynamical properties of a recently characterized chaotic attractor governing the dynamics of tumor cells interacting with healthy tissue cells and effector cells of the immune system. By using the theory of symbolic dynamics, we first characterize the topological entropy and the parameter space ordering of kneading sequences from one-dimensional iterated maps identified in the dynamics, focusing on the effects of inactivation interactions between both effector and tumor cells. The previous analyses are complemented with the computation of the spectrum of Lyapunov exponents, the fractal dimension and the predictability of the chaotic attractors. Our results show that the inactivation rate of effector cells by the tumor cells has an important effect on the dynamics of the system. The increase of effector cells inactivation involves an inverse Feigenbaum (i.e. period-halving bifurcation) scenario, which results in the stabilization of the dynamics and in an increase of dynamics predictability. Our analyses also reveal that, at low inactivation rates of effector cells, tumor cells undergo strong, chaotic fluctuations, with the dynamics being highly unpredictable. Our findings are discussed in the context of tumor cells potential viability.por
dc.identifier.citationDUARTE, Jorge; JANUARIO, Cristina; RODRIGUES, Carla; SARDANYES, Josep - Topological Complexity and Predictability in the Dynamics of a Tumor Growth Model with Shilnikov's Chaos. International Journal of Bifurcation and Chaos. ISSN 0218-1274. Vol. 23, nr. 7 (2013).por
dc.identifier.issn0218-1274
dc.identifier.other10.1142/S0218127413501241
dc.identifier.urihttp://hdl.handle.net/10400.21/2857
dc.language.isoengpor
dc.peerreviewedyespor
dc.publisherWorld Scientific Publ CO PTE LTDpor
dc.relationFCT
dc.relation.ispartofseries;1350124
dc.subjectCancerpor
dc.subjectTumor cell dynamicspor
dc.subjectChaospor
dc.subjectComplex systemspor
dc.subjectTopological entropypor
dc.subjectPredictabilitypor
dc.subjectDouble scrollpor
dc.subjectImmunotherapypor
dc.subjectAttractorspor
dc.subjectSystemspor
dc.subjectCellspor
dc.titleTopological Complexity and Predictability in the Dynamics of a Tumor Growth Model with Shilnikov's Chaospor
dc.typejournal article
dspace.entity.typePublication
oaire.citation.conferencePlaceSingaporepor
oaire.citation.issue7por
oaire.citation.titleInternational Journal of Bifurcation and Chaospor
oaire.citation.volume23por
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.latestForDiscovery4dbec82a-caa4-4662-b156-af73687e867f

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