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Hopf bifurcations in a class of reaction-diffusion equations including two discrete time delays: An algorithm for determining Hopf bifurcation, and its applications

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dc.contributor.author Bilazeroğlu, Şeyma
dc.contributor.author Merdan, H.
dc.date.accessioned 2022-05-20T12:03:09Z
dc.date.available 2022-05-20T12:03:09Z
dc.date.issued 2021-01
dc.identifier.citation Bilazeroğlu, Şeyma; Merdan, H. (2021). "Hopf bifurcations in a class of reaction-diffusion equations including two discrete time delays: An algorithm for determining Hopf bifurcation, and its applications", Chaos, Solitons and Fractals, Vol. 142. tr_TR
dc.identifier.issn 0960-0779
dc.identifier.uri http://hdl.handle.net/20.500.12416/5524
dc.description.abstract We analyze Hopf bifurcation and its properties of a class of system of reaction-diffusion equations involving two discrete time delays. First, we discuss the existence of periodic solutions of this class under Neumann boundary conditions, and determine the required conditions on parameters of the system at which Hopf bifurcation arises near equilibrium point. Bifurcation analysis is carried out by choosing one of the delay parameter as a bifurcation parameter and fixing the other in its stability interval. Second, some properties of periodic solutions such as direction of Hopf bifurcation and stability of bifurcating periodic solution are studied through the normal form theory and the center manifold reduction for functional partial differential equations. Moreover, an algorithm is developed in order to determine the existence of Hopf bifurcation (and its properties) of variety of system of reaction-diffusion equations that lie in the same class. The benefit of this algorithm is that it puts a very complex and long computations of existence of Hopf bifurcation for each equation in that class into a systematic schema. In other words, this algorithm consists of the conditions and formulae that are useful for completing the existence analysis of Hopf bifurcation by only using coefficients in the characteristic equation of the linearized system. Similarly, it is also useful for determining the direction analysis of the Hopf bifurcation merely by using the coefficients of the second degree Taylor polynomials of functions in the right hand side of the system. Finally, the existence of Hopf bifurcation for three different problems whose governing equations stay in that class is given by utilizing the algorithm derived, and thus the feasibility of the algorithm is presented. © 2020 Elsevier Ltd tr_TR
dc.language.iso eng tr_TR
dc.relation.isversionof 10.1016/j.chaos.2020.110391 tr_TR
dc.rights info:eu-repo/semantics/closedAccess tr_TR
dc.subject Delay Differential Equations tr_TR
dc.subject Discrete Time Delays tr_TR
dc.subject Functional Partial Differential Equations tr_TR
dc.subject Hopf Bifurcation tr_TR
dc.subject Periodic Solutions tr_TR
dc.subject Reaction-Diffusion System tr_TR
dc.subject Stability tr_TR
dc.title Hopf bifurcations in a class of reaction-diffusion equations including two discrete time delays: An algorithm for determining Hopf bifurcation, and its applications tr_TR
dc.type article tr_TR
dc.relation.journal Chaos, Solitons and Fractals tr_TR
dc.contributor.authorID 49206 tr_TR
dc.identifier.volume 142 tr_TR
dc.contributor.department Çankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik Bölümü tr_TR


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