共查询到16条相似文献,搜索用时 125 毫秒
1.
利用单模激光Lorenz系统实现混沌反控制 总被引:1,自引:0,他引:1
利用Lyapunov函数方法,对混沌反控制问题进行了研究.以单模激光Lorenz系统和描述心脏搏动的Bonhoeffer-Van der Pol系统为例,设计了一种控制器,成功地使Bonhoeffer-Van der Pol系统混沌化.给出了控制器的具体设计方案以及单模激光Lorenz系统与Bonhoeffer-Van der Pol系统状态之间误差系统的结构.仿真结果表明,在控制器的作用下,Bonhoeffer-Van der Pol系统所有状态变量严格地跟踪了单模激光Lorenz系统的混沌轨迹,对应的相空间中Bonhoeffer-Van der Pol系统的轨迹也由极限环转变为与单模激光Lorenz系统的轨迹完全相同的混沌吸引子,Bonhoeffer-Van der Pol系统严格地跟踪了单模激光Lorenz系统混沌的动态行为. 相似文献
2.
讨论简谐激励作用下含有界随机参数的双势阱Duffing-van der Pol系统的倍周期分岔现象.首先用Chebyshev 多项式逼近法将随机Duffing-van der Pol系统化成与其等价的确定性系统,然后通过等价确定性系统来探索该系统的倍周期分岔现象.数值模拟显示随机Duffing-van der Pol 系统与均值参数系统有着类似的倍周期分岔行为,同时指出,随机参数系统的倍周期分岔有其自身独有的特点.文中的主要数值结果表明Chebyshev 多项式逼近法是研究非线性随机参数系统动力学问题的一种有效方法.
关键词:
Chebyshev多项式
随机Duffing-van der Pol系统
倍周期分岔 相似文献
3.
研究了一类随机van der Pol 系统的Hopf分岔行为.首先根据Hilbert空间的正交展开理论,含有随机参数的van der Pol系统被约化为等价确定性系统,然后利用确定性分岔理论分析了等价系统的Hopf分岔,得出了随机van der Pol 系统的Hopf 分岔临界点,探究了随机参数对系统Hopf分岔的影响.最后利用数值模拟验证了理论分析结果.
关键词:
随机van der Pol系统
Hopf分岔
正交多项式逼近 相似文献
4.
应用 Chebyshev 多项式逼近法研究了谐和激励作用下具有随机参数的随机van der Pol系统 的倍周期分岔现象.随机系统首先被转化成等价的确定性系统,然后通过数值方法求得响应 ,借此探索了随机van der Pol系统丰富的随机倍周期分岔现象.数值模拟显示随机van der Pol 系统存在与确定性系统极为相似的倍周期分岔行为,但受随机因素的影响,又有与之不 同之处.数值结果表明,Chebyshev 多项式逼近是研究非线性系统动力学问题的一种新的有 效方法.
关键词:
Chebyshev 多项式
随机van der Pol 系统
倍周期分岔 相似文献
5.
研究了谐和激励下含有界随机参数Duffing系统(简称随机Duffing系统)中的随机混沌及其延迟反馈控制问题.借助Gegenbauer多项式逼近理论,将随机Duffing系统转化为与其等效的确定性非线性系统.这样,随机Duffing系统在谐和激励下的混沌响应及其控制问题就可借等效的确定性非线性系统来研究.分析阐明了随机混沌的主要特点,并采用Wolf算法计算等效确定性非线性系统的最大Lyapunov指数,以判别随机Duffing系统的动力学行为.数值计算表明,恰当选取不同的反馈强度和延迟时间,可分别达到抑制或诱发系统混沌的目的,说明延迟反馈技术对随机混沌控制也是十分有效的.
关键词:
随机Duffing系统
延迟反馈控制
随机混沌
Gegenbauer多项式 相似文献
6.
研究了Lévy稳定噪声激励下的双稳Duffing-van der Pol振子,利用Monte Carlo方法,得到了振幅的稳态概率密度函数.分析了Lévy稳定噪声的强度和稳定指数对概率密度函数的影响,通过稳态概率密度的性质变化,讨论了噪声振子的随机分岔现象,发现了不仅系统参数和噪声强度可以视为分岔参数,Lévy噪声的稳定指数 α 的改变也能诱导系统出现随机分岔现象.
关键词:
Lévy稳定噪声
Duffing-van der Pol振子
稳态概率密度函数
随机分岔 相似文献
7.
针对随机相位作用的Duffing混沌系统, 研究了随机相位强度变化时系统混沌动力学的演化行为及伴随的随机共振现象. 结合Lyapunov指数、庞加莱截面、相图、时间历程图、功率谱等工具, 发现当噪声强度增大时, 系统存在从混沌状态转化为有序状态的过程, 即存在噪声抑制混沌的现象, 且在这一过程中, 系统亦存在随机共振现象, 而且随机共振曲线上最优的噪声强度恰为噪声抑制混沌的参数临界点. 通过含随机相位周期力的平均效应分析并结合系统的分岔图, 探讨了噪声对混沌运动演化的作用机理, 解释了在此过程中随机共振的形成机理, 论证了噪声抑制混沌与随机共振的相互关系. 相似文献
8.
9.
探讨了非周期力(有界噪声或混沌驱动力)在非线性动力系统混沌控制中的影响.以一类典型的含有五次非线性项的Duffing-van der Pol系统为范例,通过对系统的轨道、最大Lyapunov指数、功率谱幅值及Poincar截面的分析,发现适当幅值的有界噪声或混沌信号,一方面可以消除系统对初始条件的敏感依赖性,抑制系统的混沌行为,将系统的混沌吸引子转化为奇怪非混沌吸引子;另一方面也可以诱导系统的混沌行为,将系统的周期吸引子转化为混沌吸引子.从而揭示了非周期力在混沌控制中的双重功效:抑制混沌和诱导混沌.
关键词:
混沌控制
有界噪声
混沌驱动力 相似文献
10.
利用随机光滑动力系统的Chebyshev正交多项式逼近方法,研究了双边约束条件下随机van der Pol系统的分岔现象.数值研究表明,双边约束随机van der Pol系统中不仅存在着丰富的倍周期分岔现象,还存在非光滑系统中所特有的擦边分岔.着重研究了随机非光滑系统中的擦边分岔,分析了随机因素对非光滑动力系统中擦边分岔的影响.研究表明,Chebyshev多项式逼近也是研究随机非光滑系统动力学行为的一种有效方法.
关键词:
非光滑动力系统
随机 van der Pol系统
擦边分岔
双边约束 相似文献
11.
Analysis of stochastic bifurcation and chaos in stochastic Duffing--van der Pol system via Chebyshev polynomial approximation 下载免费PDF全文
The Chebyshev polynomial approximation is applied to investigate the stochastic
period-doubling bifurcation and chaos problems of a stochastic Duffing--van
der Pol system with bounded random parameter of exponential probability
density function subjected to a harmonic excitation. Firstly the stochastic
system is reduced into its equivalent deterministic one, and then the
responses of stochastic system can be obtained by numerical methods.
Nonlinear dynamical behaviour related to stochastic period-doubling
bifurcation and chaos in the stochastic system is explored. Numerical
simulations show that similar to its counterpart in deterministic nonlinear
system of stochastic period-doubling bifurcation and chaos may occur in the
stochastic Duffing--van der Pol system even for weak intensity of random
parameter. Simply increasing the intensity of the random parameter may
result in the period-doubling bifurcation which is absent from the
deterministic system. 相似文献
12.
Stochastic period-doubling bifurcation analysis of stochastic Bonhoeffer--van der Pol system 总被引:2,自引:0,他引:2 下载免费PDF全文
In this paper, the Chebyshev polynomial approximation is applied to
the problem of stochastic period-doubling bifurcation of a stochastic
Bonhoeffer--van der Pol (BVP for short) system with a bounded random
parameter. In the analysis, the stochastic BVP system is transformed
by the Chebyshev polynomial approximation into an equivalent
deterministic system, whose response can be readily obtained by
conventional numerical methods. In this way we have explored plenty
of stochastic period-doubling bifurcation phenomena of the stochastic
BVP system. The numerical simulations show that the behaviour of the
stochastic period-doubling bifurcation in the stochastic BVP system
is by and large similar to that in the deterministic mean-parameter
BVP system, but there are still some featured differences between
them. For example, in the stochastic dynamic system the
period-doubling bifurcation point diffuses into a critical interval
and the location of the critical interval shifts with the variation
of intensity of the random parameter. The obtained results show that
Chebyshev polynomial approximation is an effective approach to
dynamical problems in some typical nonlinear systems with a bounded
random parameter of an arch-like probability density function. 相似文献
13.
应用Laguerre正交多项式逼近法研究了含有随机参数的双势阱Duffing系统的分岔和混沌行为.系统参数为指数分布随机变量的非线性动力系统首先被转化为等价的确定性扩阶系统,然后通过数值方法求得其响应.数值模拟结果的比较表明,含有随机参数的双势阱Duffing系统保持着与确定性系统相类似的倍周期分岔和混沌行为,但是由于随机因素的影响,在局部小区域内随机参数系统的动力学行为会发生突变.
关键词:
双势阱Duffing系统
指数分布概率密度函数
Laguerre多项式逼近
随机分岔 相似文献
14.
For relaxation oscillators stochastic and chaotic dynamics are investigated. The effect of random perturbations upon the period is computed. For an extended system with additional state variables chaotic behavior can be expected. As an example, the Van der Pol oscillator is changed into a third-order system admitting period doubling and chaos in a certain parameter range. The distinction between chaotic oscillation and oscillation with noise is explored. Return maps, power spectra, and Lyapunov exponents are analyzed for that purpose. 相似文献
15.
Stochastic period-doubling bifurcation analysis of a R?ssler system with a bounded random parameter 下载免费PDF全文
This paper aims to study the stochastic period-doubling
bifurcation of the three-dimensional R?ssler system with an
arch-like bounded random parameter. First, we transform the
stochastic R?ssler system into its equivalent deterministic one
in the sense of minimal residual error by the Chebyshev polynomial
approximation method. Then, we explore the dynamical behaviour of
the stochastic R?ssler system through its equivalent
deterministic system by numerical simulations. The numerical results
show that some stochastic period-doubling bifurcation, akin to the
conventional one in the deterministic case, may also appear in the
stochastic R?ssler system. In addition, we also examine the
influence of the random parameter intensity on bifurcation
phenomena in the stochastic R?ssler system. 相似文献
16.
Stochastic period-doubling bifurcation in biharmonic driven Dulling system with random parameter 下载免费PDF全文
Stochastic period-doubling bifurcation is explored in a forced Duffing system with a bounded random parameter as an additional weak harmonic perturbation added to the system. Firstly, the biharmonic driven Duffing system with a random parameter is reduced to its equivalent deterministic one, and then the responses of the stochastic system can be obtained by available effective numerical methods. Finally, numerical simulations show that the phase of the additional weak harmonic perturbation has great influence on the stochastic period-doubling bifurcation in the biharmonic driven Duffing system. It is emphasized that, different from the deterministic biharmonic driven Duffing system, the intensity of random parameter in the Duffing system can also be taken as a bifurcation parameter, which can lead to the stochastic period-doubling bifurcations. 相似文献