Bilazeroğlu, Şeyma
Loading...
Name Variants
Job Title
Dr. Öğr. Üyesi
Email Address
sbilazeroglu@cankaya.edu.tr
Main Affiliation
Matematik
Status
Current Staff
Website
ORCID ID
Scopus Author ID
Turkish CoHE Profile ID
Google Scholar ID
WoS Researcher ID
Files
Sustainable Development Goals Report Points
SDG data could not be loaded because of an error. Please refresh the page or try again later.
Scholarly Output
4
Articles
6
Citation Count
22
Supervised Theses
0
4 results
Scholarly Output Search Results
Now showing 1 - 4 of 4
Article Citation - WoS: 7Citation - Scopus: 9Hopf bifurcations in a class of reaction-diffusion equations including two discrete time delays: An algorithm for determining Hopf bifurcation, and its applications(Pergamon-elsevier Science Ltd, 2021) Bilazeroglu, S.; Bilazeroğlu, Şeyma; Merdan, H.; 49206; MatematikWe 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. (C) 2020 Elsevier Ltd. All rights reserved.Book Part Citation - WoS: 7Delay Effects on the Dynamics of the Lengyel-Epstein Reaction-Diffusion Model(Springer international Publishing Ag, 2016) Merdan, Huseyin; Bilazeroğlu, Şeyma; Kayan, Seyma; 49206; MatematikArticle Citation - WoS: 12Citation - Scopus: 13Stability 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; MatematikIn 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.Article Citation - WoS: 0Citation - Scopus: 0Effects of the random walk and the maturation period in a diffusive predator–prey system with two discrete delays(Pergamon-elsevier Science Ltd, 2023) Bilazeroglu, S.; Bilazeroğlu, Şeyma; Goktepe, S.; Merdan, H.; 49206; MatematikThis study aims to present a complete Hopf bifurcation analysis of a model describing the relationship between prey and predator. A ratio-dependent reaction-diffusion system with two discrete time delays operating under Neumann boundary conditions governs the model that represents this competition. The bifurcation parameter for the analysis is a delay parameter that reflects the amount of time needed for the predator to be able to hunt. Bilazeroglu and Merdan's algorithm (Bilazeroglu et al., 2021), which is developed by using the center manifold theorem and normal form theory, is used to establish the existence of Hopf bifurcations and also the stability of the bifurcating periodic solutions. The same procedure is used to illustrate some specific bifurcation properties, such as direction, stability, and period. Furthermore, by examining a model with constant coefficients, we also analyze how diffusion and the amount of time needed for prey to mature impact the model's dynamics. To support the obtained analytical results, we also run some numerical simulations. The results indicate that the dynamic of the mathematical model is significantly influenced by diffusion, the amount of time needed for the predator to gain the capacity to hunt, and the amount of time required for prey to reach maturity that the predator can hunt.
