Robust persistence for semidynamical systems

被引:343
作者
Smith, HL [1 ]
Zhao, XQ
机构
[1] Arizona State Univ, Dept Math, Tempe, AZ 85287 USA
[2] Mem Univ Newfoundland, Dept Math & Stat, St Johns, NF A1C 5S7, Canada
关键词
chain transitive sets; uniform persistence;
D O I
10.1016/S0362-546X(01)00678-2
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Using properties of internally chain transitive sets, we show that uniform persistence of a semi-dynamical system is robust to small perturbations of the semi-dynamical system under mild compactness conditions.
引用
收藏
页码:6169 / 6179
页数:11
相关论文
共 17 条
[1]  
Conley C., 1978, REGIONAL C SERIES MA, V38
[2]   A parabolic system modeling microbial competition in an unmixed bio-reactor [J].
Dung, L ;
Smith, HL .
JOURNAL OF DIFFERENTIAL EQUATIONS, 1996, 130 (01) :59-91
[3]   PERSISTENCE IN DISCRETE SEMIDYNAMICAL SYSTEMS [J].
FREEDMAN, HI ;
SO, JWH .
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1989, 20 (04) :930-938
[4]   UNIFORM PERSISTENCE AND CHAIN RECURRENCE [J].
GARAY, BM .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1989, 139 (02) :372-381
[5]  
Hale J. K., 1988, Asymptotic Behavior of Dissipative Systems
[6]   PERSISTENCE IN INFINITE-DIMENSIONAL SYSTEMS [J].
HALE, JK ;
WALTMAN, P .
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1989, 20 (02) :388-395
[7]  
HIRSCH MW, IN PRESS J DYNAMICAL, V13
[8]   UNIFORM PERSISTENCE AND REPELLORS FOR MAPS [J].
HOFBAUER, J ;
SO, JWH .
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1989, 107 (04) :1137-1142
[9]   ASYMPTOTICALLY AUTONOMOUS SEMIFLOWS - CHAIN RECURRENCE AND LYAPUNOV FUNCTIONS [J].
MISCHAIKOW, K ;
SMITH, H ;
THIEME, HR .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1995, 347 (05) :1669-1685
[10]   Criteria for Cr robust permanence [J].
Schreiber, SJ .
JOURNAL OF DIFFERENTIAL EQUATIONS, 2000, 162 (02) :400-426