Computer-assisted proof for two dimensional non-invertible dynamical systems

Autor: Sheng-wen Su, 蘇聖文
Rok vydání: 2007
Druh dokumentu: 學位論文 ; thesis
Popis: 95
In this paper, we present a computer-assisted technique which allows us to prove the existence of a snapback repeller for two-dimensional non-invertible dynamical systems rigorously. Firstly, we construct a finite pseudo-orbit (or a numerical orbit), which satisfies the initial point and the end point are near the fixed point. Secondly, we employ a computer-assisted study basing on shadowing to prove there exists a snapback repeller for this dynamical system. The method is applied to the discrete predator-prey model [8] which is a two dimensional non-invertible dynamical system. Finally,we use continuation methods and interval arithmetic to give computer-assisted proof that the constant gamma and the parameter value a from 5 to 4.75 which exists of snapback repellers for this dynamical system. The existence of a snapback repeller of a dynamical system implies that it has chaotic behavior [10].
Databáze: Networked Digital Library of Theses & Dissertations