Ünal Ufuktepe

Stability and invariant manifolds of a generalized Beddington host-parasitoid model

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.

Stability analysis of a host parasite model

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).MSC:39A11, 92D25.

Stability and invariant manifold for a predator-prey model with Allee effect

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 Çelik and Duman (Chaos Solitons Fractals 40:1956-1962, 2009), and Wang et al. (Ecol. Complex. 8:81-85, 2011).

Dynamical Behavior of a Cooperation Model with Allee Effect

Mutualism is an interaction between two or more species, where species derive a mutual benefit. We study the model of M.R.S. Kulenovic and M. Nurkanovic [7] by adding one of the most best-understood mechanism of Allee effect to that system which is called mate-finding. In this paper, we interpret mate-limitation of Allee effect between mutualistic species from mathematical and ecological points of view and stability analysis of the new model.

A Density Dependent Host-Parasitoid Model with Allee and Refuge Effects

A discrete-time density dependent model is studied by Sophia et al. in [3]. In this paper, we use this model and try to develop it by adding Allee and Refuge effects. With Allee Effect the intraspecific cooperation, with Refuge Effect environment heterogeneity are taken into account. We make the stability analysis of the resulting models together with some numerical simulations.

Unification of probability theory on time scales

The theory of time scales was introduced by Stefan Hilger in his PhD thesis in 1988 in order to unify continuous and discrete analysis. Probability is a discipline in which appears to be many applications of time scales. Time scales approach to probability theory unifies the standard discrete and continuous random variables. We give some basic random variables on the time scales. We define the distribution functions on time scales and show their properties.MSC: 46N30, 60B05.

Multivariable Calculus on Time Scales

Time scale analysis is the generalization of discrete and continuous analysis. In this research paper, we extend our previous study \cite{unalsinan} and develop some important concepts, tangent planes and partial derivatives for multi-variable functions on timescales with \emph{Mathematica}.

Generalization of analytic functions

Abstract 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.

Unification of calculus on Time Scales with mathematica

Abstract 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.

Hashimoto's thyroiditis with petri nets

Petri Nets (PNs)are promising tool among the various methods for modelling, analyzing and simulating biological systems. This article intents to present the basics of approach and to foster the potential role PNs could play in the development of the computational systems biology. Hashimoto’s Thyroiditis is a type of autoimmune thyroid disease in which the immune system attacks and destroys the thyroid gland. The thyroid helps set the rate of metabolism, which is the rate at which the body uses energy. Hashimoto’s stops the gland from making enough thyroid hormones for the body to work the way it should. It is the most common thyroid disease in the U.S. we give a PN model for Hashimoto’s Thyroiditis.