Lorenz系统的非线性动力学行为及仿真

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英文篇名：Nonlinear dynamical behavior and simulation of Lorenz systems 作者：刘绍刚 ; 李艳平 英文作者：LIU Shao-gang;LI Yan-ping;School of Information Science and Engineering,West Yunnan University;School of Mathematics and Information Science,Shaanxi Normal University; 关键词：超混沌 ; Lorenz系统 ; 非线性动力学行为 ; 计算机仿真 ; Lorenz平衡点 英文关键词：hyperchaos;;Lorenz system;;nonlinear dynamical behavior;;computer simulation;;Lorenz equilibrium point 中文刊名：SJSJ 英文刊名：Computer Engineering and Design 机构：滇西科技师范学院信息工程学院;陕西师范大学数学与信息科学学院; 出版日期：2019-03-16 出版单位：计算机工程与设计 年：2019 期：v.40;No.387 基金：国家自然科学基金项目(61402275);; 云南省教育厅科学研究基金指导性基金项目(2016ZDX159);; 陕西省自然科学基础研究计划基金项目(2016JM6069) 语种：中文; 页：SJSJ201903035 页数：5 CN：03 ISSN：11-1775/TP 分类号：214-218

摘要

针对非线性动力学行为的特点,利用计算机仿真技术,应用数学微分方程理论以及Matlab软件对超混沌类Lorenz系统的非线性动力学行为及其计算机仿真情况展开具体分析与探索,包括Lorenz系统数学模型及其吸引子、Lyapunov指数和维数、时序波形、功率谱、Poincare映射,以及Lorenz平衡点等。结合3种情况对超混沌类Lorenz系统的计算机仿真进行分析,整体研究成果为同步加密通信工程应用、混沌控制等提供了一定理论依据和实践支持,具有积极的理论与实践意义。
        According to the characteristics of nonlinear dynamic behavior,the nonlinear dynamic behavior of hyperchaotic Lorenz system and its computer simulation were analyzed and probed with computer simulation technology,the theory of mathematical differential equation and Matlab software,including Lorenz system mathematical model and its attractor,Lyapunov exponent and dimension,time series waveform,power spectrum,Poincare mapping,Lorenz balance point and so on.The computer simulation of the hyperchaotic Lorenz system was analyzed by combining three cases.The overall research results provide some theoretical basis and practical support for the application of synchronous encrypted communication and the control of chaos.It has positive theoretical and practical significance.

引文

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