CHAOS AND THE EFFECT OF NOISE IN A MODEL OF 3-WAVE MODE-COUPLING

被引:43
作者
HUGHES, DW
PROCTOR, MRE
机构
[1] Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, CB3 9EW, Silver Street
来源
PHYSICA D | 1990年 / 46卷 / 02期
关键词
D O I
10.1016/0167-2789(90)90034-M
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The equations governing the nonlinear interaction of three resonant waves are studied in the limit that one wave is slightly unstable, and the other two modes more heavily damped. It is shown that the dynamics can be described in terms of a bimodal one-dimensional map, which allows bifurcation sequences etc. to be simply constructed. The effect of small additive noise can be studied in the same framework; it is shown that, even at very low levels, the effect of noise can be extremely important in determining the period and amplitude of the oscillations. © 1990.
引用
收藏
页码:163 / 176
页数:14
相关论文
共 14 条
[1]   ASYMPTOTIC SOLUTIONS OF THE NON-LINEAR 3-WAVE SYSTEM [J].
BUSSAC, MN .
PHYSICAL REVIEW LETTERS, 1982, 49 (26) :1939-1942
[2]  
Busse F. H., 1984, Turbulence and Chaotic Phenomena in Fluids. Proceedings of the International Symposium, P197
[3]  
CHAPMAN PB, 1990, MATH P CAMB PHIL SOC, V108, P107
[4]  
FOWLER AC, 1984, STUD APPL MATH, V70, P215
[5]   LOCAL AND GLOBAL BEHAVIOR NEAR HOMOCLINIC ORBITS [J].
GLENDINNING, P ;
SPARROW, C .
JOURNAL OF STATISTICAL PHYSICS, 1984, 35 (5-6) :645-696
[6]   A LOW-ORDER MODEL OF THE SHEAR INSTABILITY OF CONVECTION - CHAOS AND THE EFFECT OF NOISE [J].
HUGHES, DW ;
PROCTOR, MRE .
NONLINEARITY, 1990, 3 (01) :127-153
[7]  
HUGHES DW, 1990, IN PRESS MODEL 3 WAY
[8]   SOME FLESH ON THE SKELETON - THE BIFURCATION STRUCTURE OF BIMODAL MAPS [J].
MACKAY, RS ;
TRESSER, C .
PHYSICA D, 1987, 27 (03) :412-422
[9]  
PROCTOR MRE, 1990, IN PRESS P NATO WORK
[10]  
Sparrow C., 1982, LORENZ EQUATIONS BIF