Matematik Mühendisliği Bölümü Koleksiyonu
https://hdl.handle.net/20.500.12440/98
2024-03-29T10:28:47Z
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1 of 1 Analysis of a discrete time fractional-order Vallis system
https://hdl.handle.net/20.500.12440/6148
1 of 1 Analysis of a discrete time fractional-order Vallis system
Sisman, Seyma; Merdan, Mehmet
Vallis system is a model describing nonlinear interactions of the atmosphere and temperature fluctuations with a strong influence in the equatorial part of the Pacific Ocean. As the model approaches the fractional order from the integer order, numerical simulations for different situations arise. To see the behavior of the simulations, several cases involving integer analysis with different non-integer values of the Vallis systems were applied. In this work, a fractional mathematical model is constructed using the Caputo derivative. The local asymptotic stability of the equilibrium points of the fractional-order model is obtained from the fundamental production number. The chaotic behavior of this system is studied using the Caputo derivative and Lyapunov stability theory. Hopf bifurcation is used to vary the oscillation of the system in steady and unsteady states. In order to perform these numerical simulations, we apply Grunwald-Letnikov tactics with Binomial coefficients to obtain the effects on the non-integer fractional degree and discrete time vallis system and plot the phase diagrams and phase portraits with the help of MATLAB and MAPLE packages.
2024-01-01T00:00:00Z
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MODELING DISEASE TRANSMISSION DYNAMICS WITH RANDOM DATA AND HEAVY TAILED RANDOM EFFECTS: THE ZIKA CASE
https://hdl.handle.net/20.500.12440/6057
MODELING DISEASE TRANSMISSION DYNAMICS WITH RANDOM DATA AND HEAVY TAILED RANDOM EFFECTS: THE ZIKA CASE
Bekiryazici, Zafer; Kesemen, Tülay; Merdan, Mehmet; Khaniyev, Tahir A.
In this study, we investigate a compartmental model of Zika Virus transmission under random effects. Random effects enable the analysis of random numerical characteristics of transmission, which cannot be modeled through deterministic equations. Data obtained from Zika studies in the literature are used along with heavy tailed random effects to obtain new random variables for the parameters of the deterministic model. Finally, simulations of the model are carried out to analyze the random dynamics of Zika Virus transmission. Deterministic results are compared with results from the simulations of the random system to underline the advantages of a random modeling approach. It is shown that the random model provides additional results for disease transmission dynamics such as results for standard deviation and coefficients of variation, making it a valuable alternative to deterministic modeling. Random results suggest around 90% - 120% coefficient of variation for the random model underlining the fact that the randomness should not be ignored for the transmission of this disease. © Işık University, Department of Mathematics, 2023; all rights reserved.
2023-01-01T00:00:00Z
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On the solution of random linear difference equations with Laplace transform method
https://hdl.handle.net/20.500.12440/6006
On the solution of random linear difference equations with Laplace transform method
Merdan, Mehmet; Şişman, Şeyma
In this study, Laplace transformation, which is very important for solutions to initial value problems, is examined. To solve the initial value problem of a discrete-time equation, Laplace implements the conversion method. Here, Laplace transformation is used to obtain an approach to the solutions of random difference equations formed by randomizing components of deterministic difference equations. For random behavior of linear difference equations under random effects, uniform, geometric, binomial, Poisson, and Bernouilli distributions are used, and approximate expected value, variance, standard deviation, and confidence interval of equations obtained by Laplace transformation are calculated. The results were obtained through the Maple package program. © 2023 The Authors. Mathematical Methods in the Applied Sciences published by John Wiley & Sons Ltd.
2023-01-01T00:00:00Z
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New weyl-type inequalities by multiplicative injective and surjective s-numbers of operators in reflexive banach spaces
https://hdl.handle.net/20.500.12440/5956
New weyl-type inequalities by multiplicative injective and surjective s-numbers of operators in reflexive banach spaces
Cona, Lale
In this work, two problems are investigated. In general. Weyl-type inequalities of operators in complex reflexive Banach spaces are discussed. Fir st, w'e obtained the Weyl-type inequalities using arbitrary multiplicative surjective and injective s-numbers that are dual of each other. Second, w'e introduced the Weyl-type inequalities by multiplicative injective and surjective s- numbers under certain conditions for S and S' operators hi complex reflexive Banach space. So. new Weyl-type inequalities are investigated for both dual s-number sequences and dual operators. © 2022, Adiyaman University. All rights reserved.
2022-01-01T00:00:00Z