GCRIS Repository Collection:
https://hdl.handle.net/20.500.11851/261
2024-03-28T11:12:39Z
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Domination type parameters of Pell graphs*
https://hdl.handle.net/20.500.11851/10343
Title: Domination type parameters of Pell graphs*
Authors: Özer, Arda Buğra; Saygı, Elif; Saygı, Zülfükar
Abstract: Pell graphs are defined on certain ternary strings as special subgraphs of Fibonacci cubes of odd index. In this work the domination number, total domination number, 2 -packing number, connected domination number, paired domination number, and signed domination number of Pell graphs are studied. Using integer linear programming, exact values and some estimates for these numbers of small Pell graphs are obtained. Further-more, some theoretical bounds are obtained for the domination numbers and total domina-tion numbers of Pell graphs.
2023-01-01T00:00:00Z
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Stability and bifurcation analyses of a discrete Lotka-Volterra type predator-prey system with refuge effect
https://hdl.handle.net/20.500.11851/10327
Title: Stability and bifurcation analyses of a discrete Lotka-Volterra type predator-prey system with refuge effect
Authors: Yıldız, Şevval; Bilazeroğlu, Seyma; Merdan, Huseyin
Abstract: 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.
2023-01-01T00:00:00Z
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ANALYTICALLY EXPLICIT INVERSE OF A KIND OF PERIODIC TRIDIAGONAL MATRIX USING A BACKWARD CONTINUED FRACTION APPROACH
https://hdl.handle.net/20.500.11851/9260
Title: ANALYTICALLY EXPLICIT INVERSE OF A KIND OF PERIODIC TRIDIAGONAL MATRIX USING A BACKWARD CONTINUED FRACTION APPROACH
Authors: Hopkins, T.; Kiliç, E.
Abstract: We present a fast algorithm for generating the inverse and the determinant of an extended, periodic, tridiagonal matrix. We use backward continued fractions to generate the elements of the inverse in closed form. By trading memory use against the cost of repeating the computation of certain quantities we are able to produce an effective procedure for a symbolic algebra implementation. We compare the performance of our Maple implementation with that of the standard Maple library procedures for matrix inversion and computation of the determinant on a set of illustrative example matrices. © 2022, Wilmington Scientific Publisher. All rights reserved.
2022-01-01T00:00:00Z
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The contagion dynamics of vaccine skepticism
https://hdl.handle.net/20.500.11851/9261
Title: The contagion dynamics of vaccine skepticism
Authors: Gölgeli, M.
Abstract: In this manuscript, we discuss the spread of vaccine refusal through a non-linear mathematical model involving the interaction of vaccine believers, vaccine deniers, and the media sources. Furthermore, we hypothesize that the media coverage of disease-related deaths has the potential to increase the number of people who believe in vaccines. We analyze the dynamics of the mathematical model, determine the equilibria and investigate their stability. Our theoretical approach is dedicated to emphasizing the importance of convincing people to believe in the vaccine without getting into any medical arguments. For this purpose, we present numerical simulations that support the obtained analytical results for different scenarios. © 2022, Hacettepe University. All rights reserved.
2022-01-01T00:00:00Z