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Delay Effects on the Dynamics of the Lengyel–Epstein Reaction-Diffusion Model

  • Hüseyin MerdanEmail author
  • Şeyma Kayan
Chapter
Part of the Nonlinear Systems and Complexity book series (NSCH, volume 14)

Abstract

We investigate bifurcations of the Lengyel–Epstein reaction-diffusion model involving time delay under the Neumann boundary conditions. We first give stability and Hopf bifurcation analysis of the ordinary differential equation (ODE) models, including delay associated with this model. Later, we extend this analysis to the partial differential equation (PDE) model. We determine conditions on parameters of both models to have Hopf bifurcations. Bifurcation analysis for both models show that Hopf bifurcations occur by regarding the delay parameter as a bifurcation parameter. Using the normal form theory and the center manifold reduction for partial functional differential equations, we also determine the direction of the Hopf bifurcations and the stability of bifurcating periodic solutions for the PDE model. Finally, we perform some numerical simulations to support analytical results obtained for the ODE models.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of MathematicsTOBB University of Economics and TechnologyAnkaraTurkey
  2. 2.Çankaya UniversityEtimesgutTurkey

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