具有非线性阻尼涨落的线性谐振子的随机共振

发布时间：2018-12-22 09:26

【摘要】：较之于线性噪声,非线性噪声更广泛地存在于实际系统中,但其研究远不能满足实际情况的需要.针对作为非线性阻尼涨落噪声基本构成成分的二次阻尼涨落噪声,本文考虑了周期信号与之共同作用下的线性谐振子,关注这类具有基本意义的阻尼涨落噪声的非线性对系统共振行为的影响.利用Shapiro-Loginov公式和Laplace变换推导了系统稳态响应振幅的解析表达式,并分析了稳态响应振幅的共振行为,且以数值仿真验证了理论分析的有效性.研究发现:系统稳态响应振幅关于非线性阻尼涨落噪声系数具有非单调依赖关系,特别是非线性阻尼涨落噪声比线性阻尼涨落噪声更有助于增强系统对外部周期信号的响应程度;而且,非线性阻尼涨落噪声比线性阻尼涨落噪声使得稳态响应振幅关于噪声强度具有更为丰富的共振行为;同时,二次阻尼涨落噪声使得稳态响应振幅关于系统频率出现真正的共振现象;而在这些现象和性质中,非线性噪声项的非线性性质对共振行为起着关键的作用.显然,以二次阻尼涨落作为基本形式引入的非线性阻尼涨落噪声,可以有助于提高微弱周期信号检测的灵敏度和实现对周期信号的频率估计.
[Abstract]:Compared with linear noise, nonlinear noise exists more widely in practical systems, but its research can not meet the needs of the actual situation. For the quadratic damped fluctuation noise, which is the basic component of nonlinear damped fluctuation noise, the linear harmonic oscillator acting on the periodic signal is considered in this paper. The nonlinear effects of the damped fluctuation noise on the resonance behavior of the system are investigated. The analytical expression of the steady-state response amplitude of the system is derived by using the Shapiro-Loginov formula and the Laplace transform. The resonance behavior of the steady-state response amplitude is analyzed, and the validity of the theoretical analysis is verified by numerical simulation. It is found that the steady-state response amplitude of the system has a non-monotone dependence on the nonlinear damping fluctuation noise coefficient. Especially, the nonlinear damping fluctuation noise is more helpful to enhance the response of the system to the external periodic signal than the linear damping fluctuation noise. Moreover, the nonlinear damping fluctuation noise makes the steady-state response amplitude have richer resonance behavior with respect to the noise intensity than the linear damping fluctuation noise. At the same time, the second-order damped fluctuation noise makes the steady-state response amplitude appear real resonance phenomenon in relation to the frequency of the system, and in these phenomena and properties, the nonlinear property of the nonlinear noise term plays a key role in the resonance behavior. It is obvious that the nonlinear damped fluctuation noise introduced in the form of quadratic damped fluctuation can improve the sensitivity of weak periodic signal detection and realize the frequency estimation of periodic signal.
【作者单位】：西南石油大学理学院;四川大学数学学院;
【基金】：国家自然科学基金(批准号:11171238) 四川省教育厅科研基金(批准号:14ZA0050,13ZA0191) 西南石油大学校级科技基金(批准号:2013XJZ027,2013XJZ025,2014PYZ015),西南石油大学青年教师“过学术关”资助计划(批准号:201331010049)资助的课题~~
【分类号】：O324

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