On the structural stability of discretized Burgers' equation with randomness

フォーマット:

論文

責任表示:

Hataue, Itaru

言語:

英語

出版情報:

国際情報学会 = International Information Institute, 2011-08-01

著者名:

Hataue, Itaru  

掲載情報:

Information

ISSN:

1343-4500      

巻:

14

通号:

8

開始ページ:

2585

終了ページ:

2598

バージョン:

publisher

概要:

In the present paper, we study the structural stability of discrete dynamical system from the view point of influence of randomness added to deterministic difference equations. One-dimensional Burgers' equation is discretized by central difference method and the dependence of the asymptotic structure on forcibly added randomness is studied. Both of non-conservative and conservative forms are considered. The "Sample Mean Dynamical System(SMDS)" … approach is applied in analyzing the degree of dynamical system. It is proposed that we should add a small amount of randomness to deterministic equations in order to make unstable incorrect invariant set removed in getting bifurcation diagrams. The discrete dynamical system in the case of conservative form is shown to be more unstable than that in the case of non-conservative form by analyses of SMDS. It is effective to study the structure of SMDS in evaluating the degree of structural stability of a discrete dynamical system. © 2011 International Information Institute. 続きを見る

URL:

http://hdl.handle.net/2297/31363