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Stability and Hopf Bifurcation in a delayed ratio dependent Holling-Tanner type model

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dc.contributor.authorÇelik, Canan
dc.contributor.institutionÇelik, Canan, Bahçeşehir Üniversitesi, Istanbul, Turkey
dc.date.accessioned2025-10-05T16:32:17Z
dc.date.issued2015
dc.description.abstractIn this study, a delayed ratio dependent Holling-Tanner type predator-prey model is investigated. First, the local stability of a positive equilibrium is studied and then the existence of Hopf bifurcations is established. By using the normal form theory and center manifold theorem, the explicit algorithm determining the stability, direction of the bifurcating periodic solutions are derived. Finally, we perform the numerical simulations for justifying the theoretical results. © 2015 Elsevier B.V., All rights reserved.
dc.identifier.doi10.1016/j.amc.2014.11.086
dc.identifier.endpage237
dc.identifier.issn00963003
dc.identifier.scopus2-s2.0-84923831399
dc.identifier.startpage228
dc.identifier.urihttps://doi.org/10.1016/j.amc.2014.11.086
dc.identifier.urihttps://hdl.handle.net/20.500.14719/12780
dc.identifier.volume255
dc.language.isoen
dc.publisherElsevier Inc. usjcs@elsevier.com
dc.relation.sourceApplied Mathematics and Computation
dc.subject.authorkeywordsDiscrete Delay
dc.subject.authorkeywordsHopf Bifurcation
dc.subject.authorkeywordsPredator-prey System
dc.subject.authorkeywordsStability
dc.subject.authorkeywordsBifurcation (mathematics)
dc.subject.authorkeywordsConvergence Of Numerical Methods
dc.subject.authorkeywordsPredator Prey Systems
dc.subject.authorkeywordsStability
dc.subject.authorkeywordsBifurcating Periodic Solutions
dc.subject.authorkeywordsCenter Manifold Theorem
dc.subject.authorkeywordsDiscrete Delay
dc.subject.authorkeywordsExplicit Algorithms
dc.subject.authorkeywordsLocal Stability
dc.subject.authorkeywordsNormal Form Theory
dc.subject.authorkeywordsPositive Equilibrium
dc.subject.authorkeywordsPredator-prey Modeling
dc.subject.authorkeywordsHopf Bifurcation
dc.subject.indexkeywordsBifurcation (mathematics)
dc.subject.indexkeywordsConvergence of numerical methods
dc.subject.indexkeywordsPredator prey systems
dc.subject.indexkeywordsStability
dc.subject.indexkeywordsBifurcating periodic solutions
dc.subject.indexkeywordsCenter manifold theorem
dc.subject.indexkeywordsDiscrete delay
dc.subject.indexkeywordsExplicit algorithms
dc.subject.indexkeywordsLocal stability
dc.subject.indexkeywordsNormal form theory
dc.subject.indexkeywordsPositive equilibrium
dc.subject.indexkeywordsPredator-prey modeling
dc.subject.indexkeywordsHopf bifurcation
dc.titleStability and Hopf Bifurcation in a delayed ratio dependent Holling-Tanner type model
dc.typeArticle
dcterms.referencesAkkocaoǧlu, Hande, Hopf bifurcation analysis of a general non-linear differential equation with delay, Journal of Computational and Applied Mathematics, 237, 1, pp. 565-575, (2013), Çelik, Canan, Dynamical behavior of a ratio dependent predator-prey system with distributed delay, Discrete and Continuous Dynamical Systems - Series B, 16, 3, pp. 719-738, (2011), Çelik, Canan, The stability and Hopf bifurcation for a predator-prey system with time delay, Chaos, Solitons and Fractals, 37, 1, pp. 87-99, (2008), Çelik, Canan, Hopf bifurcation of a ratio-dependent predator-prey system with time delay, Chaos, Solitons and Fractals, 42, 3, pp. 1474-1484, (2009), Chen, Xiaoxing, Periodicity in a nonlinear discrete predator-prey system with state dependent delays, Nonlinear Analysis: Real World Applications, 8, 2, pp. 435-446, (2007), Çelik, Canan, Allee effect in a discrete-time predator-prey system, Chaos, Solitons and Fractals, 40, 4, pp. 1956-1962, (2009), Fowler, Mike S., Population dynamic consequences of Allee effects, Journal of Theoretical Biology, 215, 1, pp. 39-46, (2002), Struggle for Existence, (1934), Gopalsamy, Kondalsamy, Time lags and global stability in two-species competition, Bulletin of Mathematical Biology, 42, 5, pp. 729-737, (1980), Hadjiavgousti, Despina, Allee effect in a prey-predator system, Chaos, Solitons and Fractals, 36, 2, pp. 334-342, (2008)
dspace.entity.typePublication
local.indexed.atScopus
person.identifier.scopus-author-id23034053300

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