Browsing by Author "Merdan, Huseyin"

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Citation - WoS: 7
Delay Effects on the Dynamics of the Lengyel-Epstein Reaction-Diffusion Model
(Springer international Publishing Ag, 2016) Merdan, Huseyin; Bilazeroğlu, Şeyma; Kayan, Seyma; 49206; Matematik
Citation - WoS: 0
Citation - Scopus: 1
Hopf Bifurcations of a Lengyel-Epstein Model Involving Two Discrete Time Delays
(Amer inst Mathematical Sciences-aims, 2022) Bilazeroglu, Seyma; Merdan, Huseyin; Guerrini, Luca
Hopf bifurcations of a Lengyel-Epstein model involving two discrete time delays are investigated. First, stability analysis of the model is given, and then the conditions on parameters at which the system has a Hopf bifurcation are determined. Second, bifurcation analysis is given by taking one of delay parameters as a bifurcation parameter while fixing the other in its stability interval to show the existence of Hopf bifurcations. The normal form theory and the center manifold reduction for functional differential equations have been utilized to determine some properties of the Hopf bifurcation including the direction and stability of bifurcating periodic solution. Finally, numerical simulations are performed to support theoretical results. Analytical results together with numerics present that time delay has a crucial role on the dynamical behavior of Chlorine Dioxide-Iodine-Malonic Acid (CIMA) reaction governed by a system of nonlinear differential equations. Delay causes oscillations in the reaction system. These results are compatible with those observed experimentally.
Citation - WoS: 12
Citation - Scopus: 13
Stability and bifurcation analyses of a discrete Lotka–Volterra type predator–prey system with refuge effect
(Elsevier, 2023) Yildiz, Sevval; Bilazeroğlu, Şeyma; Bilazeroglu, Seyma; Merdan, Huseyin; 49206; Matematik
In this paper, we discuss the complex dynamical behavior of a discrete Lotka-Volterra type predator-prey model including refuge effect. The model considered is obtained from a continuous-time population model by utilizing the forward Euler method. First of all, we nondimensionalize the system to continue the analysis with fewer parameters. And then, we determine the fixed points of the dimensionless system. We investigate the dynamical behavior of the system by performing the local stability analysis for each fixed point, separately. Moreover, we analytically show the existence of flip and Neimark-Sacker bifurcations at the positive fixed point by applying the normal form theory and the center manifold theorem. Bifurcation analyses are carried out by choosing the integral step size as a bifurcation parameter. In addition, we perform numerical simulations to support and extend the analytical results. All these analyses have been done for the models with and without the refuge effect to examine the effect of refuge on the dynamics. We have concluded that the refuge has significant role on the dynamical behavior of a discrete system. Furthermore, numerical simulations underline that the large integral step size causes the chaotic behavior. (c) 2022 Elsevier B.V. All rights reserved.