Geometric singular perturbation theory with real noise

被引：16

作者：

Li, Ji ^{[1
]}

Lu, Kening ^{[2
,3
]}

Bates, Peter W. ^{[1
]}

机构：

[1] Michigan State Univ, Dept Math, E Lansing, MI 48824 USA

[2] Brigham Young Univ, Dept Math, Provo, UT 84602 USA

[3] Sichuan Univ, Sch Math, Chengdu 610064, Sichuan, Peoples R China

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2015年 / 259卷 / 10期

基金：

美国国家科学基金会;

关键词：

Random dynamical systems; Random normally hyperbolic invariant manifolds; Random stable and unstable foliations; Random singular perturbation; Boundary condition; Random inclination; TRACKING INVARIANT-MANIFOLDS; NERNST-PLANCK SYSTEMS; EXCHANGE LEMMAS; ASYMPTOTIC STABILITY; PERSISTENCE;

D O I：

10.1016/j.jde.2015.06.023

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove the existence of families of random invariant manifolds for singularly perturbed systems of ordinary differential equations with sufficiently small real noise. We use these invariant manifolds to prove a random version of the inclination theorem or exchange lemma. Published by Elsevier Inc.

引用

页码：5137 / 5167

页数：31

共 23 条

[1] [Anonymous], 1988, APPL MATH SCI
[2] Arnold L, 1998, Random dynamical systems
[3] C′-inclination theorems for singularly perturbed equations
Brunovsky, P
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 1999, 155 (01) : 133 - 152
[4] Brunovsky P., 1996, ACTA MATH U COMENIAN, V1, P23
[5] HOMOCLINIC BIFURCATIONS WITH NONHYPERBOLIC EQUILIBRIA
DENG, B
[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1990, 21 (03) : 693 - 720
[6] Eckhaus W., 1973, Matched asymptotic expansions and singular perturbations
[7] Poisson-Nernst-Planck systems for ion channels with permanent charges
Eisenberg, Bob
Liu, Weishi
[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2007, 38 (06) : 1932 - 1966
[8] GEOMETRIC SINGULAR PERTURBATION-THEORY FOR ORDINARY DIFFERENTIAL-EQUATIONS
FENICHEL, N
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 1979, 31 (01) : 53 - 98
[9] FENICHEL N, 1971, INDIANA U MATH J, V21, P193
[10] ASYMPTOTIC STABILITY WITH RATE CONDITIONS
FENICHEL, N
[J]. INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1974, 23 (12) : 1109 - 1137

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