本文選題：簡(jiǎn)諧噪聲 + 隨機(jī)共振�。� 參考：《昆明理工大學(xué)》2017年碩士論文

【摘要】：隨機(jī)動(dòng)力系統(tǒng)中噪聲的激勵(lì)會(huì)使系統(tǒng)出現(xiàn)許多有趣的動(dòng)力學(xué)行為。無論是噪聲的建設(shè)性作用還是系統(tǒng)本身對(duì)外部調(diào)節(jié)的響應(yīng)都受到了人們的普遍關(guān)注。本文研究了簡(jiǎn)諧噪聲驅(qū)動(dòng)下隨機(jī)雙穩(wěn)系統(tǒng)的動(dòng)力學(xué)行為。首先在第一章分別介紹了電路系統(tǒng)中非線性行為、隨機(jī)共振及噪聲增強(qiáng)穩(wěn)定性和相干共振的研究背景和研究現(xiàn)狀。接著第二章介紹了相關(guān)的隨機(jī)理論及研究方法。最后第三章和第四章分析了簡(jiǎn)諧噪聲對(duì)的雙穩(wěn)系統(tǒng)的動(dòng)力學(xué)行為的影響,研究結(jié)果如下:第三章研究了簡(jiǎn)諧噪聲和小周期信號(hào)驅(qū)動(dòng)下的雙穩(wěn)系統(tǒng),結(jié)果表明:(1)當(dāng)簡(jiǎn)諧噪聲參數(shù)r固定時(shí),我們發(fā)現(xiàn)噪聲強(qiáng)度D和簡(jiǎn)諧噪聲參數(shù)Ω可以影響功率譜品質(zhì)因子β。β越大時(shí),隨機(jī)共振現(xiàn)象越明顯。此外,β的峰值隨著噪聲強(qiáng)度的增大向著Ω增大的方向移動(dòng);(2)當(dāng)簡(jiǎn)諧噪聲參數(shù)Ω固定時(shí),在不同的噪聲強(qiáng)度D下我們同樣可以通過調(diào)節(jié)參數(shù)r的大小來得到隨機(jī)共振現(xiàn)象;(3)通過調(diào)節(jié)噪聲強(qiáng)度D、簡(jiǎn)諧噪聲參數(shù)Γ和Ω的取值,系統(tǒng)的隨機(jī)共振現(xiàn)象的強(qiáng)弱可以得到控制。接著,我們考慮了兩個(gè)關(guān)聯(lián)的簡(jiǎn)諧噪聲激發(fā)的雙穩(wěn)系統(tǒng),并分析了噪聲增強(qiáng)穩(wěn)定性現(xiàn)象,研究結(jié)果表明:(1)在簡(jiǎn)諧噪聲參數(shù)Ω固定時(shí),系統(tǒng)的平均滯留時(shí)間T在不同的參數(shù)r下都會(huì)存在峰值,即噪聲增強(qiáng)穩(wěn)定性.并且隨著參數(shù)r的增加,滯留時(shí)間曲線的峰值會(huì)向著乘性噪聲強(qiáng)度Q增加的方向移動(dòng);(2)當(dāng)簡(jiǎn)諧噪聲參數(shù)r固定時(shí),隨著參數(shù)Ω的增加,系統(tǒng)平均滯留時(shí)間T的峰值也會(huì)隨著乘性噪聲強(qiáng)度Q增加的方向移動(dòng)。這意味著簡(jiǎn)諧噪聲對(duì)隨機(jī)共振和噪聲增強(qiáng)穩(wěn)定性的控制起著關(guān)鍵的作用。第四章研究了單個(gè)簡(jiǎn)諧噪聲對(duì)無周期信號(hào)驅(qū)動(dòng)的雙穩(wěn)系統(tǒng)的動(dòng)力學(xué)行為影響,結(jié)果表明:(1)系統(tǒng)的特征關(guān)聯(lián)時(shí)間∧隨著簡(jiǎn)諧噪聲參數(shù)Ω會(huì)出現(xiàn)一個(gè)峰值,并隨著r的增大朝著參數(shù)Ω減小的方向發(fā)生移動(dòng);(2)當(dāng)噪聲強(qiáng)度d固定時(shí),系統(tǒng)的特征關(guān)聯(lián)時(shí)間∧隨著參數(shù)r也會(huì)出現(xiàn)一個(gè)峰值,并隨著Ω的增大朝著參數(shù)r減小的方向發(fā)生移動(dòng)。類相干共振現(xiàn)象也可以得到控制;(3)當(dāng)其他條件固定時(shí),參數(shù)Ω的增加會(huì)減小特征關(guān)聯(lián)時(shí)間的峰值,而參數(shù)r的增加則會(huì)增大特征關(guān)聯(lián)時(shí)間的峰值。這意味著簡(jiǎn)諧噪聲對(duì)類相干共振的控制同樣也起著關(guān)鍵的作用。
[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.
【學(xué)位授予單位】：昆明理工大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O19

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本文編號(hào)：1863191