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

• Main Authors: Sheng-wen Su, 蘇聖文
• Other Authors: Chen-Chang Peng, Ph.D.
• Format: Others
• Language: en_US
• Published: 2007
• Online Access: http://ndltd.ncl.edu.tw/handle/45125072059614205814

碩士 === 國立嘉義大學 === 應用數學系研究所 === 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].