Unstable periodic orbits and discretization cycles

被引：8

作者：

Binder, PM ^{[1
]}

Okamoto, NH ^{[1
]}

机构：

[1] Univ Hawaii, Dept Phys & Astron, Hilo, HI 96720 USA

来源：

PHYSICAL REVIEW E | 2003年 / 68卷 / 04期

关键词：

D O I：

10.1103/PhysRevE.68.046206

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：

Limit cycles that arise from discretizing the variable(s) of a nonlinear map are generally found to shadow individual unstable periodic orbits (UPOs) of the corresponding continuous map. In a few cases the discretization cycles can only be explained with other mechanisms, such as the near-occurrence of an UPO, or crossover between two or more UPOs.

引用

收藏

页数：3

相关论文

共 21 条

[1] Counting and classifying attractors in high dimensional dynamical systems [J].

Bagley, RJ ;

Glass, L .

JOURNAL OF THEORETICAL BIOLOGY, 1996, 183 (03) :269-284

[2] EFFECTS OF PHASE-SPACE DISCRETIZATION ON THE LONG-TIME BEHAVIOR OF DYNAMIC-SYSTEMS [J].

BECK, C ;

ROEPSTORFF, G .

PHYSICA D, 1987, 25 (1-3) :173-180

[3] LIMIT-CYCLES IN A QUADRATIC DISCRETE ITERATION [J].

BINDER, PM .

PHYSICA D, 1992, 57 (1-2) :31-38

[4] SIMULATING CHAOTIC BEHAVIOR WITH FINITE-STATE MACHINES [J].

BINDER, PM ;

JENSEN, RV .

PHYSICAL REVIEW A, 1986, 34 (05) :4460-4463

[5] MACHINE ITERATION OF A LINEAR FUNCTION - LOCAL BEHAVIOR [J].

BINDER, PM .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 1991, 21 (2-3) :133-140

[6] Invertibility of dynamical systems in granular phase space [J].

Binder, PM ;

Idrobo, JC .

PHYSICAL REVIEW E, 1998, 58 (06) :7987-7989

[7] Chaos and experimental resolution [J].

Binder, PM ;

Cuéllar, MC .

PHYSICAL REVIEW E, 2000, 61 (04) :3685-3688

[8] Statistical laws for computational collapse of discretized chaotic mappings [J].

Diamond, P ;

Pokrovskii, A .

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 1996, 6 (12A) :2389-2399

[9] EXACT NUMERICAL-STUDIES OF HAMILTONIAN MAPS - ITERATING WITHOUT ROUNDOFF ERROR [J].

EARN, DJD ;

TREMAINE, S .

PHYSICA D, 1992, 56 (01) :1-22

[10] ROUNDOFF-INDUCED PERIODICITY AND THE CORRELATION DIMENSION OF CHAOTIC ATTRACTORS [J].

GREBOGI, C ;

OTT, E ;

YORKE, JA .

PHYSICAL REVIEW A, 1988, 38 (07) :3688-3692