Stability and bifurcation in a delayed predator-prey model with Holling-type IV response function and age structure

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dc.contributor.authorCai, Yuting
dc.contributor.authorWang, Chuncheng
dc.contributor.authorFan, Dejun
dc.date.accessioned2021-08-26T16:59:14Z
dc.date.available2021-08-26T16:59:14Z
dc.date.issued2021-05-14
dc.description.abstractIn this article, we study a predator-prey model with age structure, Holling-type IV response, and two time delays. By an algebraic method, we determine all the critical values for these two delays, such that the characteristic equation has purely imaginary roots. This provides a sharp stability region on the parameter plane of the positive equilibrium. Applying integrated semigroup theory and Hopf bifurcation theorem for abstract Cauchy problems with non-dense domain, we can show the occurrence of Hopf bifurcation as the time delays pass through these critical values. In particular, the phenomenon of stability switches can also be observed as the time delays vary. Numerical simulations are carried out to illustrate the theoretical results.
dc.description.departmentMathematics
dc.formatText
dc.format.extent16 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationCai, Y., Wang, C., & Fan, D. (2021). Stability and bifurcation in a delayed predator-prey model with Holling-type IV response function and age structure. <i>Electronic Journal of Differential Equations, 2021</i>(42), pp. 1-16.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/14452
dc.language.isoen
dc.publisherTexas State University, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 2021, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectAge-structured model
dc.subjectHopf bifurcation
dc.subjectHolling-type IV response
dc.titleStability and bifurcation in a delayed predator-prey model with Holling-type IV response function and age structure
dc.typeArticle

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