具有反馈控制离散Logistic系统的分支分析

伍代勇

doi:10.13371/j.cnki.chin.q.j.m.2015.01.008

数学季刊 >

2015 , Vol. 30 >Issue 1: 66 - 78

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2015.01.008

具有反馈控制离散Logistic系统的分支分析

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Department of Mathematics, Anqing Normal University

Wu Dai-yong(1979-), male, native of Xiantao, Hubei, an associate professor of Anqing Normal University, M.S.D., engages in biomathematics.

收稿日期: 2013-04-10

网络出版日期: 2020-11-24

基金资助

Supported by the Scientific Research Programmes of Colleges in Anhui(KJ2013Z186)；

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Bifurcation Analysis of a Discrete Logistic System with Feedback Control

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Department of Mathematics, Anqing Normal University

Wu Dai-yong(1979-), male, native of Xiantao, Hubei, an associate professor of Anqing Normal University, M.S.D., engages in biomathematics.

Received date: 2013-04-10

Online published: 2020-11-24

Supported by

Supported by the Scientific Research Programmes of Colleges in Anhui(KJ2013Z186)；

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摘要

The paper studies the dynamical behaviors of a discrete Logistic system with feedback control. The system undergoes Flip bifurcation and Hopf bifurcation by using the center manifold theorem and the bifurcation theory. Numerical simulations not only illustrate our results, but also exhibit the complex dynamical behaviors of the system, such as the period-doubling bifurcation in periods 2, 4, 8 and 16, and quasi-periodic orbits and chaotic sets.

关键词： feedback control; Logistic system; discrete; Flip bifurcation; Hopf bifurcation

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伍代勇 . 具有反馈控制离散Logistic系统的分支分析[J]. 数学季刊, 2015 , 30(1) : 66 -78 . DOI: 10.13371/j.cnki.chin.q.j.m.2015.01.008

Abstract

Key words： feedback control; Logistic system; discrete; Flip bifurcation; Hopf bifurcation

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