Browsing by Author "Kapcak, Sinan"

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Generalization of Analytic Functions
(Elsevier Science Inc, 2011) Kapcak, Sinan; Ufuktepe, Ünal
The concept of analyticity for complex functions on time scale complex plane was introduced by Bohner and Guseinov in 2005. They developed completely delta differentiability, delta analytic functions on products of two time scales, and Cauchy-Riemann equations for delta case. In this research paper we study on continuous, discrete and semi-discrete analytic functions and developed completely nabla differentiability, nabla analytic functions on products of two time scales, and Cauchy-Riemann equations for nabla case. (C) 2011 Elsevier Inc. All rights reserved.
Citation - WoS: 5
Citation - Scopus: 11
Stability Analysis of a Host Parasite Model
(Springer International Publishing Ag, 2013) Ufuktepe, Unal; Kapcak, Sinan
Host parasite models are similar to host parasitoid models except that the parasite does not necessarily kill the host. Leslie/Gower model (Leslie and Gower in Biometrika 47(3/4):219-234, 1960) played a historical role in ecology. We consider the stability of Misra and Mitra's model (Misra and Mitra in Comput. Math. Appl. 52: 525-538, 2006). We study this system analytically and improve the results of Misra and Mitra (Comput. Math. Appl. 52: 525-538, 2006).
Stability and Bifurcation of Predator-Prey Models With the Allee Effect
(İzmir Ekonomi Üniversitesi, 2013) Kapcak, Sinan; Ufuktepe, Ünal; Elaydı, Saber
Birbirinden farklı popülasyonların etkileşiminin en iyi bilinen örneklerinden biri Nicholson-Bailey konakçı-parazitoid modelidir. Bu, bir parazitoid ve konakçısından oluşan, doğrusal olmayan bir kesikli-zaman modelidir. Beddington ve arkadaşları, Nicholson-Bailey modelinin, konakçı sayısının lojistik olarak büyüdüğü, yoğunluğa bağlı versiyonunu araştırmışlardır. Yine aynı sistemin gerçekçi başka bir hali Hone, Irle ve Thurura tarafından modellenmiştir. Bu modelde, faz düzleminde, iki popülasyon da asimtotik olarak sabit noktalara veya invaryant bir eğriye yakınsayabiliyor. Bu tezde, Beddington modelinin genelleştirilmiş halini ve bu modelin Allee etkisi altındaki dinamiklerini araştıracağız. Keywords: discrete dynamical systems, beddington model, allee e?ect, stability, invariant curves, bifurcation.
Citation - WoS: 3
Citation - Scopus: 6
Stability and Invariant Manifold for a Predator-Prey Model With Allee Effect
(Springer International Publishing Ag, 2013) Ufuktepe, Unal; Kapcak, Sinan; Akman, Olcay
Predator-prey models are similar to host-parasite and host-parasitoid models. We investigate the stability and invariant manifolds of a discrete predator-prey model by using center manifold theory which is not addressed in Celik and Duman (Chaos Solitons Fractals 40: 1956-1962, 2009), and Wang et al. (Ecol. Complex. 8: 81-85, 2011).
Citation - WoS: 21
Citation - Scopus: 26
Stability and Invariant Manifolds of a Generalized Beddington Host-Parasitoid Model
(Taylor & Francis Ltd, 2013) Kapcak, Sinan; Ufuktepe, Unal; Elaydi, Saber
We will investigate the stability and invariant manifolds of a new discrete host-parasitoid model. It is a generalization of the Beddington-Nicholson-Bailey model. Our study establishes analytically, for the first time, the stability of the coexistence fixed point.
Unification of Calculus on Time Scales With Mathematica
(Elsevier Science Inc, 2011) Ufuktepe, Ünal; Kapcak, Sinan
In 1990 Hilger defined the Time Scale Calculus which is the unification of discrete and continuous analysis in his PhD. In 2005 Yantir and Ufuktepe showed delta derivative with Mathematica [5]. In this study we give many computations of Time Scale Calculus with Mathematica such as the numerical and symbolic computation of forward jump operator and delta derivative for a particular time scale, graphs of functions, and definite integral on a time scale. We also improve and extent the Time Scale package for symbolics computations. (C) 2011 Elsevier Inc. All rights reserved.