Ünal Ufuktepe

article

Stability analysis of a prey refuge predator–prey model with Allee effects

Unal Ufuktepe, Burcin Kulahcioglu, Olcay Akman

Journal of Biosciences > 2019 > 44 > 4 > 1-9

We constructed a discrete-time predator–prey model by adding prey refuge and Allee effects (predator saturation on prey and mate limitation on predator) to an earlier prey–predator model and examined its dynamics. We show the existence of positive fixed points and study the stability properties. The numerical simulations and bifurcation diagrams verify the impact of refuge and the Allee mechanism...

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Applications of Graph Coloring

Ünal Ufuktepe, Goksen Bacak

Lecture Notes in Computer Science > Computational Science and Its Applications – ICCSA 2005 > Symbolic Computation, SC 2005 Workshop > 522-528

A graph G is a mathematical structure consisting of two sets V(G) (vertices of G) and E(G) (edges of G). Proper coloring of a graph is an assignment of colors either to the vertices of the graphs, or to the edges, in such a way that adjacent vertices / edges are colored differently. This paper discusses coloring and operations on graphs with Mathematica and webMathematica. We consider many classes...

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e-Calculus at IZTECH

Ünal Ufuktepe, Günnur Ufuktepe, Asli Deniz, Veli Dündar

Lecture Notes in Computer Science > Technologies for E-Learning and Digital Entertainment > E-Learning System and Graphics Education > 243-250

In today’s new economy, characterized by industrial revolutions, globalization and information technology changes traditional classroom and teaching methods. Calculus is the basic course for the fresher at university. Mathematics has a negative development at universities and colleges. The number of students taking mathematics courses and those successfully passing the exams are rapidly decreasing...

chapter

Mathematica Applications on Time Scales

Ahmet Yantır, Ünal Ufuktepe

Lecture Notes in Computer Science > Computational Science and Its Applications – ICCSA 2005 > Symbolic Computation, SC 2005 Workshop > 529-537

Stefan Hilger introduced the calculus on time scales in order to unify continuous and discrete analysis in 1988. The study of dynamic equations is an active area of research since time scales unifies both discrete and continuous processes, besides many others. In this paper we give many examples on derivative and integration on time scales calculus with Mathematica. We conclude with solving the first...

chapter

Hashimoto’s Thyroiditis with Petri Nets

Ünal Ufuktepe, Buket Yılmaz

Lecture Notes in Computer Science > Computational Science and Its Applications – ICCSA 2010 > Workshop on Biomathematics, Bioinformatics and Biostatistics (IBBB 2010) > 53-61

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...

chapter

Measure on Time Scales with Mathematica

Ünal Ufuktepe, Ahmet Yantır

Lecture Notes in Computer Science > Computational Science – ICCS 2006 > Poster Session II > 916-919

In this paper we study the Lebesgue Δ-measure on time scales. We refer to [3, 4] for the main notions and facts from the general measure and Lebesgue Δ integral theory. The objective of this paper is to show how the main concepts of Mathematica can be applied to fundamentals of Lebesgue Δ- and Lebesgue $\nabla$ - measure on an arbitrary time scale and also on a discrete time scale whose rule is...

chapter

An Application with webMathematica

Ünal Ufuktepe

Lecture Notes in Computer Science > Computational Science — ICCS 2003 > Russian Track > 774-780

There have been many technological dawns in the last 30 years, during which the desktop computer and the Internet have been developed. The importance of Internet in education, particularly using its Web is a well-recognized fact. A wealth of resources and techniques now exist which serve as a source both for exciting examples of new teaching practices, as well as easily accessible methods for adoption...

chapter

Graph Coloring with webMathematica

Ünal Ufuktepe, Goksen Bacak, Tina Beseri

Lecture Notes in Computer Science > Computational Science - ICCS 2004 > Workshop on Computer Algebra Systems and Applications (CASA 2004) > 376-381

Coloring of a graph is an assignment of colors either to the edges of the graph G, or to vertices, or to maps in such a way that adjacent edges/vertices/maps are colored differently. We consider the problem of coloring graphs by using webMathematica which is the new web-based technology. In this paper, we describe some web-based interactive examples on graph coloring with webMathematica.

chapter

Basic Calculus on Time Scale with Mathematica

Ahmet Yantır, Ünal Ufuktepe

Lecture Notes in Computer Science > Computational Science — ICCS 2003 > Russian Track > 821-827

Mathematical modeling of time dependent systems are always interesting for applied mathematicians. First continuous and then discrete mathematical modeling are built during the mathematical development from ancient to the modern times. By the discovery of the time scales, the problem of irregular controlling of time dependent systems is solved in 1990’s. In this paper, we explain the derivative of...

article

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

Ünal Ufuktepe, Sinan Kapçak, Olcay Akman

Advances in Difference Equations > 2013 > 2013 > 1 > 1-8

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).

article

Stability analysis of a host parasite model

Ünal Ufuktepe, Sinan Kapçak

Advances in Difference Equations > 2013 > 2013 > 1 > 1-7

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...

article

Unification of probability theory on time scales

Ünal Ufuktepe

Advances in Difference Equations > 2012 > 2012 > 1 > 1-13

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...

article

Generalization of analytic functions

Sinan Kapcak, Ünal Ufuktepe

Applied Mathematics and Computation > 2011 > 218 > 3 > 851-855

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...

article

Unification of calculus on Time Scales with mathematica

Ünal Ufuktepe, Sinan Kapçak

Applied Mathematics and Computation > 2011 > 218 > 3 > 1102-1106

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...

chapter

Multivariable Calculus on Time Scales

Sinan Kapcak, Ünal Ufuktepe

2011 International Conference on Computational Science and Its Applications > 41 - 50

2011 International Conference on Computational Science and Its Applications (ICCSA)

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}.

article

Applying Mathematica and webMathematica to graph coloring

Ünal Ufuktepe, Goksen Bacak

Future Generation Computer Systems > 2007 > 23 > 5 > 716-720

This paper analyzes some graph issues by using the symbolic program Mathematica and its version for the Web, webMathematica. In particular, we consider the problem of graph coloring: the assignment of colors to the vertices/edges of the graph such that adjacent vertices/edges are colored differently. In addition, we address the problem of obtaining the tenacity of binomial trees with Mathematica....

INFONA - science communication portal

Search results for: Ünal Ufuktepe

Stability analysis of a prey refuge predator–prey model with Allee effects

Applications of Graph Coloring

e-Calculus at IZTECH

Mathematica Applications on Time Scales

Hashimoto’s Thyroiditis with Petri Nets

Measure on Time Scales with Mathematica

An Application with webMathematica

Graph Coloring with webMathematica

Basic Calculus on Time Scale with Mathematica

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

Stability analysis of a host parasite model

Unification of probability theory on time scales

Generalization of analytic functions

Unification of calculus on Time Scales with mathematica

Multivariable Calculus on Time Scales

Applying Mathematica and webMathematica to graph coloring

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