简谐噪声驱动下双稳系统中的动力学行为研究

发布时间：2018-05-08 21:42

本文选题：简谐噪声 + 随机共振　；参考：《昆明理工大学》2017年硕士论文

【摘要】：随机动力系统中噪声的激励会使系统出现许多有趣的动力学行为。无论是噪声的建设性作用还是系统本身对外部调节的响应都受到了人们的普遍关注。本文研究了简谐噪声驱动下随机双稳系统的动力学行为。首先在第一章分别介绍了电路系统中非线性行为、随机共振及噪声增强稳定性和相干共振的研究背景和研究现状。接着第二章介绍了相关的随机理论及研究方法。最后第三章和第四章分析了简谐噪声对的双稳系统的动力学行为的影响,研究结果如下:第三章研究了简谐噪声和小周期信号驱动下的双稳系统,结果表明:(1)当简谐噪声参数r固定时,我们发现噪声强度D和简谐噪声参数Ω可以影响功率谱品质因子β。β越大时,随机共振现象越明显。此外,β的峰值随着噪声强度的增大向着Ω增大的方向移动;(2)当简谐噪声参数Ω固定时,在不同的噪声强度D下我们同样可以通过调节参数r的大小来得到随机共振现象;(3)通过调节噪声强度D、简谐噪声参数Γ和Ω的取值,系统的随机共振现象的强弱可以得到控制。接着,我们考虑了两个关联的简谐噪声激发的双稳系统,并分析了噪声增强稳定性现象,研究结果表明:(1)在简谐噪声参数Ω固定时,系统的平均滞留时间T在不同的参数r下都会存在峰值,即噪声增强稳定性.并且随着参数r的增加,滞留时间曲线的峰值会向着乘性噪声强度Q增加的方向移动;(2)当简谐噪声参数r固定时,随着参数Ω的增加,系统平均滞留时间T的峰值也会随着乘性噪声强度Q增加的方向移动。这意味着简谐噪声对随机共振和噪声增强稳定性的控制起着关键的作用。第四章研究了单个简谐噪声对无周期信号驱动的双稳系统的动力学行为影响,结果表明:(1)系统的特征关联时间∧随着简谐噪声参数Ω会出现一个峰值,并随着r的增大朝着参数Ω减小的方向发生移动;(2)当噪声强度d固定时,系统的特征关联时间∧随着参数r也会出现一个峰值,并随着Ω的增大朝着参数r减小的方向发生移动。类相干共振现象也可以得到控制;(3)当其他条件固定时,参数Ω的增加会减小特征关联时间的峰值,而参数r的增加则会增大特征关联时间的峰值。这意味着简谐噪声对类相干共振的控制同样也起着关键的作用。
[Abstract]:The excitation of noise in stochastic dynamical system will lead to many interesting dynamic behaviors. Both the constructive effect of noise and the response of the system to external regulation have been paid more and more attention. In this paper, the dynamical behavior of stochastic bistable system driven by harmonic noise is studied. In the first chapter, the background and research status of nonlinear behavior, stochastic resonance, noise enhanced stability and coherent resonance are introduced respectively. Then the second chapter introduces the related random theory and research methods. Finally, in the third and fourth chapters, the influence of harmonic noise on the dynamic behavior of the bistable system is analyzed. The results are as follows: in Chapter 3, the bistable system driven by simple harmonic noise and small periodic signal is studied. The results show that when the simple harmonic noise parameter r is fixed, we find that the noise intensity D and the harmonic noise parameter 惟 can affect the power spectrum quality factor 尾. The larger the power spectrum quality factor 尾, the more obvious the stochastic resonance is. In addition, the peak value of 尾 moves towards the direction of 惟 increasing with the increase of noise intensity) when the harmonic noise parameter 惟 is fixed, Under different noise intensity D, we can also obtain stochastic resonance by adjusting the magnitude of parameter r.) by adjusting the value of noise intensity D, simple harmonic noise parameter 螕 and 惟, the strength of stochastic resonance phenomenon of the system can be controlled. Then, we consider two correlated bistable systems excited by harmonic noise, and analyze the phenomenon of noise enhanced stability. The results show that: 1) when the harmonic noise parameter 惟 is fixed, The mean residence time T of the system has a peak value at different parameters r, that is, noise enhancement stability. And with the increase of parameter r, the peak value of residence time curve will move towards the direction of multiplicative noise intensity Q increasing. When the parameter r of harmonic noise is fixed, the peak value of retention time curve will increase with the increase of parameter 惟. The peak value of the mean residence time T also moves in the direction of increasing the intensity of multiplicative noise Q. This means that harmonic noise plays a key role in the control of stochastic resonance and noise enhancement stability. In chapter 4, we study the effect of single harmonic noise on the dynamic behavior of bistable systems driven by aperiodic signals. The results show that the characteristic correlation time of the system is a peak value with the harmonic noise parameter 惟. When the noise intensity d is fixed, the characteristic correlation time of the system also appears a peak value with the parameter r. And with the increase of 惟, it moves towards the direction of decreasing parameter r. The quasi-coherent resonance phenomenon can also be controlled. When other conditions are fixed, the increase of parameter 惟 will decrease the peak value of characteristic correlation time, while the increase of parameter r will increase the peak value of characteristic correlation time. This means that harmonic noise also plays a key role in the control of quasi-coherent resonance.
【学位授予单位】：昆明理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O19

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