河北师范大学学报—

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刊名：河北师范大学学报（自然科学版）Journal of Hebei Normal University (Natural Science)
主办：河北师范大学
ISSN： 1000-5854
CN： 13-1061/N
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概周期驱动分段Logistic系统的奇异非混沌吸引子

沈云柱¹

张凡辉¹

东广霞²

1. 济南大学数学科学学院, 山东济南 250022;
2. 山东体育学院体育运动学校, 山东济南 250022
DOI： 10.13763/j.cnki.jhebnu.nse.2019.03.004

Strange Nonchaotic Attractors in Quasiperiodically Piecewise Logistic System

SHEN Yunzhu¹, ZHANG Fanhui¹, DONG Guangxia²

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摘要/Abstract

摘要：

鉴于对非光滑系统奇异非混沌吸引子（SNAs）的形成原因与诞生机理的认识尚不清楚，以概周期驱动分段Logistic非光滑系统为研究对象，分析此系统中存在的多种类型的奇异非混沌吸引子，通过应用最大李雅普诺夫指数、相敏感指数方法辨识了奇异非混沌吸引子的诞生机理，主要包括Heagy-Hammel路线、间歇Ⅰ路线、分形化路线，研究结果发现，奇异非混沌吸引子在非光滑系统中的存在类型比较丰富.研究结果可为研究非光滑系统中的奇异非混沌吸引子提供理论参考.

Abstract：

It is not clear that the current understanding of the formation and mechanism of nonsmooth system for strange nonchaotic attractors(SNAs).We focuses on the quasiperiodic driven for Logistic system,aiming to analyze the various types of strange nonchaotic driven piecewise Logistic attractors by applying the largest Lyapunov exponents and phase-sensitive exponents in this system.It mainly includes the Heagy-Hammel routes,the type-I intermittency routes and the fractalization routes.The results of the study show that these types of strange nonchaotic attractors are abundant in nonsmooth systems and the results provide a theoretical basis for the study of strange nonchaotic attractors in nonsmooth systems.

关键词

关键词： 非光滑系统 ; 奇异非混沌吸引子 ; 最大李雅普诺夫指数 ; 相敏感指数

Key words： nonsmooth system ; strange nonchaotic attractor ; the largest Lyapunov exponent ; phase sensitivity exponent

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