Sensitive dependence on parameters of continuous-time nonlinear dynamical systems

被引：1

作者：

Medeiros, E. S. ^{[1
,2
]}

Caldas, I. L. ^{[1
]}

Baptista, M. S. ^{[2
]}

机构：

[1] Univ Sao Paulo, Inst Phys, Rua Matao,Travessa R 187, BR-05508090 Sao Paulo, Brazil

[2] Univ Aberdeen, Inst Complex Syst & Math Biol, SUPA, Aberdeen AB24 3UE, Scotland

来源：

CHAOS SOLITONS & FRACTALS | 2017年 / 99卷

基金：

巴西圣保罗研究基金会;

关键词：

Fractal boundaries; Parameters space; Complex periodic windows; BIFURCATION STRUCTURES; TRANSIENT CHAOS; CIRCUIT; OSCILLATORS; SPACE; MODEL;

D O I：

10.1016/j.chaos.2017.03.043

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The sensitive dependence of periodicity and chaos on parameters is investigated for three-dimensional nonlinear dynamical systems. Previous works have found that noninvertible low-dimensional maps present power-law exponents relating the uncertainty between periodicity and chaos to the precision on the system parameters. Furthermore, the values obtained for these exponents have been conjectured to be universal in these maps. However, confirmation of the observed exponent values in continuous time systems remain an open question. In this work, we show that one of these exponents can also be found in different classes of three-dimensional continuous-time dynamical systems, suggesting that the sensitive dependence on parameters of deterministic nonlinear dynamical systems is typical. (C) 2017 Elsevier Ltd. All rights reserved.

引用

页码：16 / 19

页数：4

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