一类含周期激励Duffing系统的数值模拟
Numerical Simulation of a Class of Duffing Systems with Periodic Excitation
DOI: 10.12677/DSC.2021.101009, PDF,    国家自然科学基金支持
作者: 李 亮, 钱有华*：浙江师范大学数学与计算机科学学院，浙江 金华
关键词: Duffing系统；阻尼系数；混沌现象；四阶Runge-Kutta算法；Duffing System； Damping Coefficient； Chaotic Phenomenon； Fourth-Order Runge-Kutta Algorithm
摘要: 本文主要探究一类有周期激励的Duffing系统，根据Melnikov方法、欧拉离散、四阶Runge-Kutta算法理论及Matlab程序等进行数值模拟。从理论上分析不同参数下系统的动力学现象，如分岔、周期运动、混沌运动等，作出时间序列图、相图、分岔图及最大Lyapunov指数图，观测在振幅、频率及阻尼项变化时Duffing系统产生的复杂动态行为。数值模拟发现，在考虑激励振幅和频率不变时，随阻尼项的增大，系统混沌行为会发生显著变化，混沌状态将逐渐消失形成周期运动，而在考虑振幅影响时，系统混沌状态则无明显改变。
Abstract: This paper mainly explores a Duffing system with periodic excitation. Based on Melnikov method, Euler discretization, fourth-order Runge-Kutta algorithm theory and Matlab program, it theoretically analyzes the dynamic phenomena of the system under different parameters, such as bifurcation, periodic motion and chaos, makes time series diagram, phase diagram, bifurcation diagram and maximum Lyapunov index diagram, and observes Duffing system when amplitude, frequency and damping terms change. Numerical simulation shows that when the excitation amplitude and frequency are constant, with the increase of damping term, the chaotic behavior of the system will change significantly, and the chaotic state will gradually disappear to form periodic motion, while when the influence of amplitude is considered, the chaotic state of the system will not change much.
文章引用：李亮, 钱有华. 一类含周期激励Duffing系统的数值模拟[J]. 动力系统与控制, 2021, 10(1): 77-90. https://doi.org/10.12677/DSC.2021.101009

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