PROBABILISTIC APPROACH TO HOMOCLINIC CHAOS

被引：4

作者：

DAEMS, D ^{[1
]}

NICOLIS, G ^{[1
]}

机构：

[1] UNIV LIBRE BRUXELLES,CTR NONLINEAR PHENOMENA & COMPLEX SYST,B-1050 BRUSSELS,BELGIUM

来源：

JOURNAL OF STATISTICAL PHYSICS | 1994年 / 76卷 / 5-6期

关键词：

HOMOCLINIC CHAOS; DISCRETE MAPS; FROBENIUS-PERRON EQUATION; GENERALIZED COARSE-GRAINING; MASTER EQUATION; TIME AUTOCORRELATION FUNCTION;

D O I：

10.1007/BF02187063

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

Three-dimensional systems posessing a homoclinic orbit associated to a saddle focus with eigenvalues rho +/- iomega, -lambda and giving rise to homoclinic chaos when the Shil'nikov condition rho < lambda is satisfied are studied. The 2D Poincare map and its 1D contractions capturing the essential features of the flow are given. At homoclinicity, these 1D maps are found to be piecewise linear. This property allows one to reduce the Frobenius-Perron equation to a master equation whose solution is analytically known. The probabilistic properties such as the time autocorrelation function of the state variable x are explicitly derived.

引用

页码：1287 / 1305

页数：19

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