STATIONARY PROBABILITY-DISTRIBUTION NEAR STABLE LIMIT-CYCLES FAR FROM HOPF-BIFURCATION POINTS

被引：22

作者：

DYKMAN, M ^{[1
]}

CHU, XL ^{[1
]}

ROSS, J ^{[1
]}

机构：

[1] STANFORD UNIV,DEPT CHEM,STANFORD,CA 94305

来源：

PHYSICAL REVIEW E | 1993年 / 48卷 / 03期

关键词：

D O I：

10.1103/PhysRevE.48.1646

中图分类号：

O35 [流体力学]; O53 [等离子体物理学];

学科分类号：

070204 ; 080103 ; 080704 ;

摘要：

We obtain analytic results for the stationary probability distribution in the vicinity of a stable limit cycle for Markov systems described by a Fokker-Planck equation or a birth-death master equation. The results apply best for ranges of parameters removed from Hopf bifurcation points. As a by-product, we demonstrate that there holds a Liouville-like theorem for the stationary probability distribution: the product of the velocity along the limit cycle times the area of the cross section of the probability distribution transverse to the cycle is a constant. A numerical simulation of a chemical model system with a limit cycle shows good agreement with the analytic results.

引用

页码：1646 / 1654

页数：9

共 17 条

[1]

[Anonymous], 1984, SPRINGER SERIES SYNE

[2]

EBELING W, 1983, STUD BIOPHYS, V98, P147

[3] TIME-PERIODIC OSCILLATIONS IN A MODEL FOR THE RESPIRATORY PROCESS OF A BACTERIAL CULTURE [J].