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Chaotic Motions of the van der Pol-Duffing Oscillator Subjected to Periodic External and Parametric Excitations with Delayed Feedbacks
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作者 Liang-qiang ZHOU Fang-qi CHEN 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2024年第4期1111-1126,共16页
Chaotic dynamics of the van der Pol-Duffing oscillator subjected to periodic external and parametric excitations with delayed feedbacks are investigated both analytically and numerically in this manuscript.With the Me... Chaotic dynamics of the van der Pol-Duffing oscillator subjected to periodic external and parametric excitations with delayed feedbacks are investigated both analytically and numerically in this manuscript.With the Melnikov method,the critical value of chaos arising from homoclinic or heteroclinic intersections is derived analytically.The feature of the critical curves separating chaotic and non-chaotic regions on the excitation frequency and the time delay is investigated analytically in detail.The monotonicity of the critical value to the excitation frequency and time delay is obtained rigorously.It is presented that there may exist a special frequency for this system.With this frequency,chaos in the sense of Melnikov may not occur for any excitation amplitudes.There also exists a uncontrollable time delay with which chaos always occurs for this system.Numerical simulations are carried out to verify the chaos threshold obtained by the analytical method. 展开更多
关键词 van der pol-duffing oscillator time delay CHAOS parametric excitation Melnikov method
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Adaptive backstepping control and synchronization of a modified and chaotic Van der Pol-Duffing oscillator 被引量:4
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作者 U.E.VINCENT R.K.ODUNAIKE +1 位作者 J.A.LAOYE A.A.GBINDINNINUOLA 《控制理论与应用(英文版)》 EI 2011年第2期273-277,共5页
In this paper,we propose a backstepping approach for the synchronization and control of modified Van-der Pol Duffing oscillator circuits.The method is such that one controller function that depends essentially on avai... In this paper,we propose a backstepping approach for the synchronization and control of modified Van-der Pol Duffing oscillator circuits.The method is such that one controller function that depends essentially on available circuit parameters that is sufficient to drive the two coupled circuits to a synchronized state as well achieve the global stabilization of the system to its regular dynamics.Numerical simulations are given to demonstrate the effectiveness of the technique. 展开更多
关键词 CHAOS SYNCHRONIZATION Back-stepping van der pol-duffing oscillator
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PRINCIPAL RESPONSE OF VAN DER POL-DUFFING OSCILLATOR UNDER COMBINED DETERMINISTIC AND RANDOM PARAMETRIC EXCITATION
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作者 戎海武 徐伟 +2 位作者 王向东 孟光 方同 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2002年第3期299-310,共12页
The principal resonance of Van der Pol-Duffing oscillator to combined deterministic and random parametric excitations is investigated. The method of multiple scales was used to determine the equations of modulation of... The principal resonance of Van der Pol-Duffing oscillator to combined deterministic and random parametric excitations is investigated. The method of multiple scales was used to determine the equations of modulation of amplitude and phase. The behavior, stability and bifurcation of steady state response were studied. Jumps were shown to occur under some conditions. The effects of damping, detuning, bandwidth, and magnitudes of deterministic and random excitations are analyzed. The theoretical analysis were verified by numerical results. 展开更多
关键词 principal resonance van der pol-duffing oscillator multiple scate method largest Lyapunov exponent steady state probability density function
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耦合Van der Pol-Duffing振子的动力学分析 被引量:6
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作者 李群宏 陆启韶 《河南师范大学学报(自然科学版)》 CAS CSCD 2002年第4期15-18,共4页
非线性耦合VanderPol -Duffing振子在强共振情形下具有极其复杂的动力学行为 ,本文利用数值方法研究了各系统参数对振子系统动力学性态的影响 ,揭示了减幅、增幅、周期。
关键词 van der pol-duffing振子 动力学 非线性耦合 van der pol-duffing方程 强共振 分岔 混沌 非线性振动系统
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谐和与随机噪声联合作用下VanderPol-Duffing振子的参数主共振 被引量:5
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作者 戎海武 徐伟 +2 位作者 王向东 孟光 方同 《应用数学和力学》 CSCD 北大核心 2002年第3期273-282,共10页
研究了VanderPol_Duffing振子在谐和与随机噪声联合激励下的参数主共振响应和稳定性问题· 用多尺度法分离了系统的快变项 ,并求出了系统的最大Liapunov指数和稳态概率密度函数 ,还分析了失稳、分叉和跳跃现象 ,讨论了系统的阻尼... 研究了VanderPol_Duffing振子在谐和与随机噪声联合激励下的参数主共振响应和稳定性问题· 用多尺度法分离了系统的快变项 ,并求出了系统的最大Liapunov指数和稳态概率密度函数 ,还分析了失稳、分叉和跳跃现象 ,讨论了系统的阻尼项、非线性项。 展开更多
关键词 参数主共振 van-der-pol-duffing振子 多尺度法 谐和噪声 激励 随机噪声
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简谐与随机噪声联合激励下Van der Pol-Duffing系统的响应 被引量:3
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作者 戎海武 王向东 +2 位作者 孟光 徐伟 方同 《振动工程学报》 EI CSCD 北大核心 2003年第4期502-505,共4页
研究了 Van der Pol-Duffing振子在简谐与随机噪声联合激励下的响应问题。用参数变换法使方程出现小参数 ,用多尺度法分离系统的快变项 ,讨论系统的阻尼项、非线性项和随机项等参数对系统响应的影响。理论分析和数值模拟表明 ,当随机激... 研究了 Van der Pol-Duffing振子在简谐与随机噪声联合激励下的响应问题。用参数变换法使方程出现小参数 ,用多尺度法分离系统的快变项 ,讨论系统的阻尼项、非线性项和随机项等参数对系统响应的影响。理论分析和数值模拟表明 ,当随机激励强度增大时 ,系统的响应可从一个极限环变为一个扩散的极限环 ;在一定的条件下 ,系统可有两个稳定的稳态解及随机跳跃现象。 展开更多
关键词 van der Pol—Duffing振子 简谐运动 随机噪声激励 参数变换法 多尺度法 非线性振动
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一个Van Der Pol-Duffing系统的混沌与控制 被引量:3
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作者 李飞 方见树 《湖南城市学院学报(自然科学版)》 CAS 2009年第4期29-32,共4页
研究了Van der Pol-Duffing振子的混沌动力学行为,应用直接微扰法构造了系统的通解,由该通解获得了预测混沌出现的Melnikov判据.在非微扰情形,相图和相应Poincaré截面的演化结果表明:系统阻尼和外驱动力的变化都可以导致系统由倍... 研究了Van der Pol-Duffing振子的混沌动力学行为,应用直接微扰法构造了系统的通解,由该通解获得了预测混沌出现的Melnikov判据.在非微扰情形,相图和相应Poincaré截面的演化结果表明:系统阻尼和外驱动力的变化都可以导致系统由倍周期分叉进入混沌状态,当频率参数取相同值时,系统混沌被完全抑制. 展开更多
关键词 van der pol-duffing方程 MELNIKOV函数 混沌 混沌控制
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改进型Van der Pol-Duffing混沌振子的同步研究
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作者 王绍明 王安福 《武汉科技大学学报》 CAS 2007年第5期538-541,共4页
研究了改进型Van der Pol-Duffing混沌振子的同步问题。当驱动系统的参数已知时,根据Lyapunov稳定性理论,设计了一个线性反馈控制器,使两个相同的改进型Van der Pol-Duffing混沌振子同步,并得出了保守性较小的同步条件;当驱动系统的参... 研究了改进型Van der Pol-Duffing混沌振子的同步问题。当驱动系统的参数已知时,根据Lyapunov稳定性理论,设计了一个线性反馈控制器,使两个相同的改进型Van der Pol-Duffing混沌振子同步,并得出了保守性较小的同步条件;当驱动系统的参数未知时,利用自适应控制方法,选择了适当的自适应律,构造了两个简单的控制器,使响应系统与驱动系统同步,并同时实现了驱动系统中未知参数的辨识。通过数值仿真,表明了这些方法的有效性。 展开更多
关键词 同步 van der pol-duffing混沌振子 线性反馈 自适应控制
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广义分数阶van der Pol-Duffing振子的动力学响应与隔振效果研究 被引量:5
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作者 唐建花 李向红 +2 位作者 王敏 申永军 李壮壮 《振动与冲击》 EI CSCD 北大核心 2022年第1期10-18,共9页
用平均法研究了含分数阶导数项的van der Pol-Duffing振子的动力学行为和力传递率。得到了主共振时振子的一阶解析解、定常解幅频曲线和相频曲线的解析表达式,进一步通过与数值解作对比,验证了解析解的正确性,分析了不同参数对幅频曲线... 用平均法研究了含分数阶导数项的van der Pol-Duffing振子的动力学行为和力传递率。得到了主共振时振子的一阶解析解、定常解幅频曲线和相频曲线的解析表达式,进一步通过与数值解作对比,验证了解析解的正确性,分析了不同参数对幅频曲线和力传递率的影响。结果表明:解析解与数值解吻合良好;在无量纲情况下,共振区分数阶项系数、非线性参数、分数阶阶次、阻尼比对幅频曲线和力传递率的共振峰值均有抑制作用;不同频率区段参数对隔振效果的影响不同,在低频隔振区非线性参数和幅值越小隔振效果越好,此外阻尼比对力传递率影响很小;在高频隔振区增大非线性参数、幅值和阻尼比有助于提高隔振效果。 展开更多
关键词 平均法 van der pol-duffing振子 主共振 力的传递率
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控制周期激励Van der Pol-Duffing振子的混沌 被引量:2
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作者 崔春霞 吴锋民 《浙江工业大学学报》 CAS 2004年第3期266-268,共3页
对周期激励VanderPol-Duffing振子进行了研究:x··-μ(1-x2)x·-αx+βx3=fcosωt。首先运用相图分析、直接观察运动时间序列的方法发现,VanderPol-Duffing振子在一定条件下会出现混沌行为。在实际工程中,混沌行为往往会... 对周期激励VanderPol-Duffing振子进行了研究:x··-μ(1-x2)x·-αx+βx3=fcosωt。首先运用相图分析、直接观察运动时间序列的方法发现,VanderPol-Duffing振子在一定条件下会出现混沌行为。在实际工程中,混沌行为往往会导致振荡或不规则运动,甚至主系统的彻底崩溃,因此有必要抑制系统的混沌行为。文中采用周期激振力法对系统中的混沌行为进行了控制,并结合lyapunov指数谱进行了分析,结果表明VanderPol-Duffing振子中的混沌运动得到了有效的控制。 展开更多
关键词 van der pol-duffing振子 周期激振力 混沌控制 LYAPUNOV指数 混沌运动 非线性动力学
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A modified averaging scheme with application to the secondary Hopf bifurcation of a delayed van der Pol oscillator 被引量:9
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作者 Z.H.Wang H.Y.Hu 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2008年第4期449-454,共6页
In this paper, a modified averaging scheme is presented for a class of time-delayed vibration systems with slow variables. The new scheme is a combination of the averaging techniques proposed by Hale and by Lehman and... In this paper, a modified averaging scheme is presented for a class of time-delayed vibration systems with slow variables. The new scheme is a combination of the averaging techniques proposed by Hale and by Lehman and Weibel, respectively. The averaged equation obtained from the modified scheme is simple enough but it retains the required information for the local nonlinear dynamics around an equilibrium. As an application of the present method, the delay value for which a secondary Hopf bifurcation occurs is successfully located for a delayed van der Pol oscillator. 展开更多
关键词 Time delay ·Secondary Hopf bifurcation·The averaging technique van der Pol oscillator
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基于耦合Van der Pol-Duffing系统的微弱信号检测研究 被引量:3
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作者 石兆羽 杨绍普 赵志宏 《中国测试》 CAS 北大核心 2018年第8期107-112,119,共7页
传统方法检测微弱信号具有一定的困难,利用混沌振子对微弱信号敏感以及对强噪声具有良好免疫力的特性,提出基于耦合Van der Pol-Duffing振子系统检测微弱信号的新方法。对比不同参数下耦合系统的动力学行为,通过分岔图和二分法确定临界... 传统方法检测微弱信号具有一定的困难,利用混沌振子对微弱信号敏感以及对强噪声具有良好免疫力的特性,提出基于耦合Van der Pol-Duffing振子系统检测微弱信号的新方法。对比不同参数下耦合系统的动力学行为,通过分岔图和二分法确定临界阈值,保证阈值搜索速度和阈值精度。阐述基于相图的微弱信号检测原理,通过从混沌态到周期态的转变成功检测淹没在强噪声中的微弱信号,信噪比门限达到–30 d B。同时考察不同精度幅值下噪声对系统状态的影响,不同频率信号以及相移对检测的影响。仿真结果表明,该耦合系统在强噪声条件下对微弱信号敏感,用于检测微弱信号是可行的。 展开更多
关键词 耦合系统 van der pol-duffing振子 混沌 微弱信号检测
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时滞耦合van der Pol-Duffing振子环的动力学分析 被引量:3
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作者 施添添 茅晓晨 《动力学与控制学报》 2019年第3期264-269,共6页
研究含时滞的大规模van der Pol-Duffing耦合振子系统的非线性动力学.通过讨论特征方程根分布情况确定系统的稳定性,并在耦合时滞和强度平面上给出振幅死亡区域.结合数值算例,揭示同步和异步周期振荡、概周期运动以及混沌吸引子等现象.... 研究含时滞的大规模van der Pol-Duffing耦合振子系统的非线性动力学.通过讨论特征方程根分布情况确定系统的稳定性,并在耦合时滞和强度平面上给出振幅死亡区域.结合数值算例,揭示同步和异步周期振荡、概周期运动以及混沌吸引子等现象.基于非线性振子电路和时滞电路,构建电路实验平台,有效验证理论和数值结果.研究结果表明,时滞可以显著影响系统动力学特性,如诱发振幅死亡、稳定性切换以及复杂振荡等. 展开更多
关键词 时滞 van der pol-duffing振子 同步 振幅死亡 复杂动力学
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含平方项和5次幂项的Van der Pol-Duffing系统混沌控制 被引量:1
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作者 张莉 彭建奎 《兰州文理学院学报(自然科学版)》 2019年第1期1-5,共5页
研究了同时含有平方项和高次幂项的Van der Pol-Duffing系统的混沌行为及混沌控制问题,数值仿真分析了该系统存在的典型非线性动力学行为.主要采用单初始点分岔分析方法、最大Lyapunov指数和Poincare映射方法,从不同侧面揭示了在周期激... 研究了同时含有平方项和高次幂项的Van der Pol-Duffing系统的混沌行为及混沌控制问题,数值仿真分析了该系统存在的典型非线性动力学行为.主要采用单初始点分岔分析方法、最大Lyapunov指数和Poincare映射方法,从不同侧面揭示了在周期激振力作用下系统的周期运动、混沌运动,以及运动形式的演化过程,并用x|x|控制方法实现了系统的混沌抑制问题. 展开更多
关键词 van der pol-duffing振子 混沌控制 最大LYAPUNOV指数 POINCARE截面
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RESPONSE OF PARAMETRICALLY EXCITED DUFFING-VAN DER POL OSCILLATOR WITH DELAYED FEEDBACK 被引量:1
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作者 李欣业 陈予恕 +1 位作者 吴志强 宋涛 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2006年第12期1585-1595,共11页
The dynamical behaviour of a parametrically excited Duffing-van der Pol oscillator under linear-plus-nonlinear state feedback control with a time delay is concerned. By means of the method of averaging together with t... The dynamical behaviour of a parametrically excited Duffing-van der Pol oscillator under linear-plus-nonlinear state feedback control with a time delay is concerned. By means of the method of averaging together with truncation of Taylor expansions, two slow-flow equations on the amplitude and phase of response were derived for the case of principal parametric resonance, it is shown that the stability condition for the trivial solution is only associated with the linear terms in the original systems besides the amplitude and frequency of parametric excitation. And the trivial solution can be stabilized by appreciate choice of gains and time delay in feedback control. Different from the case of the trivial solution, the stability condition for nontrivial solutions is also associated with nonlinear terms besides linear terms in the original system. It is demonstrated that nontrivial steady state responses may lose their stability by saddle-node (SN) or Hopf bifurcation (HB) as parameters vary. The simulations, obtained by numerically integrating the original system, are in good agreement with the analytical results. 展开更多
关键词 Duffing-van der Pol oscillator principal parametric resonance time delay feedback control BIFURCATION
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Impulsive Control for T-S Fuzzy Model Based Chaotic Systems Consisting of Van der Pol Oscillators Coupled to Linear Oscillators 被引量:2
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作者 Qi-Shui Zhong Jing-Fu Bao Zhu-Sheng Kang 《Journal of Electronic Science and Technology of China》 2007年第4期348-351,共4页
This paper proposes an impulsive control scheme for chaotic systems consisting of Van der Pol oscillators coupled to linear oscillators (VDPL) based on their Takagi-Sugeno (T-S) fuzzy models. A T-S fuzzy model is ... This paper proposes an impulsive control scheme for chaotic systems consisting of Van der Pol oscillators coupled to linear oscillators (VDPL) based on their Takagi-Sugeno (T-S) fuzzy models. A T-S fuzzy model is utilized to represent the chaotic VDPL system. By using comparison method, a general asymptotical stability criterion by means of linear matrix inequality (LMI) is derived for the T-S fuzzy model of VDPL system with impulsive effects. The simulation results demonstrate the effectiveness of the proposed scheme. 展开更多
关键词 Impulsive control T-S fuzzy model CHAOS van der Pol oscillator.
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Phase synchronization and synchronization frequency of two-coupled van der Pol oscillators with delayed coupling
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作者 Hossein Gholizade-Narm Asad Azemi Morteza Khademi 《Chinese Physics B》 SCIE EI CAS CSCD 2013年第7期79-83,共5页
In this paper, phase synchronization and the frequency of two synchronized van der Pol oscillators with delay coupling are studied. The dynamics of such a system are obtained using the describing function method, and ... In this paper, phase synchronization and the frequency of two synchronized van der Pol oscillators with delay coupling are studied. The dynamics of such a system are obtained using the describing function method, and the necessary conditions for phase synchronization are also achieved. Finding the vicinity of the synchronization frequency is the major advantage of the describing function method over other traditional methods. The equations obtained based on this method justify the phenomenon of the synchronization of coupled oscillators on a frequency either higher, between, or lower than the highest, in between, or lowest natural frequency of the aggregate oscillators. Several numerical examples simulate the different cases versus the various synchronization frequency delays. 展开更多
关键词 van der Pol oscillator delay coupling phase synchronization synchronization frequency
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Time Delay Induced Oscillation: An Example on a Class of <i>n</i>Coupled Van Der Pol Oscillators Model with Delays
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作者 Chunhua Feng Carl S. Pettis 《Applied Mathematics》 2012年第6期571-576,共6页
In this paper, a class of n coupled van der Pol oscillator model with delays is considered. By employing an analysis approach, some sufficient conditions to guarantee the existence of stability and oscillations for th... In this paper, a class of n coupled van der Pol oscillator model with delays is considered. By employing an analysis approach, some sufficient conditions to guarantee the existence of stability and oscillations for themodel are obtained. Examples are provided to demonstrate the results. 展开更多
关键词 N COUPLED van der Pol oscillator MODEL Characteristic Equation Delay oscilLATION
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Application of the Homotopy Perturbation Method to Nonlinear Heat Conduction and Fractional Van der Pol Damped Nonlinear Oscillator
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作者 T. A. Nofel 《Applied Mathematics》 2014年第6期852-861,共10页
In this paper, a powerful analytical method, called He’s homotopy perturbation method is applied to obtaining the approximate periodic solutions for some nonlinear differential equations in mathematical physics via V... In this paper, a powerful analytical method, called He’s homotopy perturbation method is applied to obtaining the approximate periodic solutions for some nonlinear differential equations in mathematical physics via Van der Pol damped non-linear oscillators and heat transfer. Illustrative examples reveal that this method is very effective and convenient for solving nonlinear differential equations. Comparison of the obtained results with those of the exact solution, reveals that homotopy perturbation method leads to accurate solutions. 展开更多
关键词 NONLINEAR oscillators HOMOTOPY Perturbation Method FRACTIONAL van der POL DAMPED NONLINEAR oscillator Heat Transfer
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Application of Van der Pol oscillator screening for peripheral arterial disease in patients with diabetes mellitus
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作者 Jianxing Wu Chianming Li +2 位作者 Weiling Chen Chiahung Lin Tainsong Chen 《Journal of Biomedical Science and Engineering》 2013年第12期1143-1154,共12页
This paper proposes a Van der Pol (VDP) oscillator screening for peripheral arterial disease (PAD) in patients with diabetes mellitus. The long-term elevated blood sugar levels produce a high risk of peripheral neurop... This paper proposes a Van der Pol (VDP) oscillator screening for peripheral arterial disease (PAD) in patients with diabetes mellitus. The long-term elevated blood sugar levels produce a high risk of peripheral neuropathy and peripheral vascular disease, especially in the foot of a diabetic. Early detection is important, in order to prevent foot problems for diabetic patients with PAD. Photoplethysmography (PPG) is a non-invasive method for the detection of blood volume changes in peripheral arteries. Because of changes in the resistance-compliance, the rise time and transit time for the PPG signals increase and change in their shape are highly correlated with PAD severity. In this study, the Burg autoregressive (AR) method is used to determine the characteristic frequencies of the right-and left-side PPG signals. For bilateral frequency spectra, the VDP oscillator uses asynchronous signals. This produces damped sinusoidal responses and the oscillation overshoot (OS) is an approximating function only of the damped factor. This index is used to estimate the degree of PAD, including normal the condition and diabetic patients with PAD. The results show that the proposed method is efficient and more accurate in the estimation of PAD. 展开更多
关键词 van der POL (VDP) oscillator PERIPHERAL ARTERIAL Disease (PAD) Burg AUTOREGRESSIVE Method oscillation OVERSHOOT
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