Browsing by Author "Kayan, S."

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Citation - WoS: 15
Citation - Scopus: 14
An Algorithm for Hopf Bifurcation Analysis of a Delayed Reaction-Diffusion Model
(Springer, 2017) Kayan, S.; Merdan, H.
We present an algorithm for determining the existence of a Hopf bifurcation of a system of delayed reaction-diffusion equations with the Neumann boundary conditions. The conditions on parameters of the system that a Hopf bifurcation occurs as the delay parameter passes through a critical value are determined. These conditions depend on the coefficients of the characteristic equation corresponding to linearization of the system. Furthermore, an algorithm to obtain the formulas for determining the direction of the Hopf bifurcation, the stability, and period of the periodic solution is given by using the Poincare normal form and the center manifold theorem. Finally, we give several examples and some numerical simulations to show the effectiveness of the algorithm proposed.
Citation - WoS: 14
Citation - Scopus: 16
Bifurcation Analysis of a Modified Tumor-Immune System Interaction Model Involving Time Delay
(Edp Sciences S A, 2017) Kayan, S.; Merdan, H.; Yafia, R.; Goktepe, S.
We study stability and Hopf bifurcation analysis of a model that refers to the competition between the immune system and an aggressive host such as a tumor. The model which describes this competition is governed by a reaction-diffusion system including time delay under the Neumann boundary conditions, and is based on Kuznetsov-Taylor's model. Choosing the delay parameter as a bifurcation parameter, we first show that Hopf bifurcation occurs. Second, we determine two properties of the periodic solution, namely its direction and stability, by applying the normal form theory and the center manifold reduction for partial functional differential equations. Furthermore, we discuss the effects of diffusion on the dynamics by analyzing a model with constant coefficients and perform some numerical simulations to support the analytical results. The results show that diffusion has an important effects on the dynamics of a mathematical model.
Citation - WoS: 25
Citation - Scopus: 22
Hopf Bifurcations in Lengyel-Epstein Reaction-Diffusion Model With Discrete Time Delay
(Springer, 2015) Merdan, H.; Kayan, S.; Kayan,
We investigate bifurcations of the Lengyel-Epstein reaction-diffusion model involving time delay under the Neumann boundary conditions. Choosing the delay parameter as a bifurcation parameter, we show that Hopf bifurcation occurs. We also determine two properties of the Hopf bifurcation, namely direction and stability, by applying the normal form theory and the center manifold reduction for partial functional differential equations.