Adaptation to the edge of chaos in the self-adjusting logistic map

被引：33

作者：

Melby, P ^{[1
]}

Kaidel, J ^{[1
]}

Weber, N ^{[1
]}

Hübler, A ^{[1
]}

机构：

[1] Univ Illinois, Dept Phys, Ctr Complex Syst Res, Urbana, IL 61801 USA

来源：

PHYSICAL REVIEW LETTERS | 2000年 / 84卷 / 26期

关键词：

D O I：

10.1103/PhysRevLett.84.5991

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

Self-adjusting, or adaptive, systems have gathered much recent interest. We present a model for self-adjusting systems which treats the control parameters of the system as slowly varying, rather than constant. The dynamics of these parameters is governed by a low-pass filtered feedback from the dynamical variables of the system. We apply this model to the logistic map and examine the behavior of the control parameter. We find that the parameter leaves the chaotic regime. We observe a high probability of finding the parameter at the boundary between periodicity and chaos. We therefore find that this system exhibits adaptation to the edge of chaos.

引用

页码：5991 / 5993

页数：3

共 10 条

[1] SELF-ORGANIZED CRITICALITY
BAK, P
TANG, C
WIESENFELD, K
[J]. PHYSICAL REVIEW A, 1988, 38 (01): : 364 - 374
[2] HAKEN H, 1978, SYNERGETICS, P191
[3] JACKSON EA, 1989, PERSPECTIVES NONLINE, P154
[4] COMPUTATION AT THE EDGE OF CHAOS - PHASE-TRANSITIONS AND EMERGENT COMPUTATION
LANGTON, CG
[J]. PHYSICA D, 1990, 42 (1-3): : 12 - 37
[5] Mitchell M, 1997, P 1 INT C EV COMP IT
[6] PACKARD NH, CCSR885 U ILL
[7] A THEORY FOR ADAPTATION AND COMPETITION APPLIED TO LOGISTIC MAP DYNAMICS
PIERRE, D
HUBLER, A
[J]. PHYSICA D, 1994, 75 (1-3): : 343 - 360
[8] RITZ T, 1996, P 1996 INT WORKSH CO, P63
[9] SCHUSTER H, 1984, DETERMINISTIC CHAOS, P7
[10] STROGATZ SH, 1994, NONLINEAR DYNAMICS C, P103

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