数理解析研究所讲究録第1909巻.PDF

数理解析研究所講究録 第 1909 巻 2014 年 207-216 207 RESEARCH ARTICLE Applications of Discrete Dynamical Systems with Mathematica \Unal Ufuktepe*, Sinan Kap\caak Izmir University of Economics, Department of Mathematics, Izmir, Turkey (Received 00 Month $200x$; ?nal version received 00 Month $200x$) Mathematica is extremely popular with a wide range of researchers from all sorts of disciplines. It is a symbolic, numerical and graphical manipulation package. In this paper we provide an introduction to the theory of discrete dynamical systems with the aid of the Mathematica for both senior undergraduates and graduate students. Mathematica applications cover the stability of the one dimensional system, the Cobweb diagram for one dimensional system, the time series diagram, the phase plane diagrams for two-dimensional systems. Applications are taken from biomathematics subjects: prey-predator models, host-parasitoid models, population dynamics, and modeling the populations of inter- acting species, bifurcation, and basin of attractions are given with codes and examples. Keywords: discrete dynamical systems, mathematica 1. Introduction Mathematica is extremely popular with a wide range of researchers from all sorts of disciplines. It is a symbolic, numerical and graphical manipulation package. This paper is both an survey on theory and techniques of discrete dynamical systems by using of the software Mathematica. This paper is intended for