本文研究了含信号调制噪声和频率波动的小时滞线性分数阶振子的随机共振.利用分数阶Shapiro-Loginov公式和Laplace变换技巧,本文首先推导了系统响应的一阶稳态矩和稳态响应振幅增益(Output Amplitude Gain, OAG)的解析表达式,然后讨论...本文研究了含信号调制噪声和频率波动的小时滞线性分数阶振子的随机共振.利用分数阶Shapiro-Loginov公式和Laplace变换技巧,本文首先推导了系统响应的一阶稳态矩和稳态响应振幅增益(Output Amplitude Gain, OAG)的解析表达式,然后讨论了分数阶、时滞和噪声参数对OAG的影响.结果显示:各参数对OAG的影响均呈现非单调变化的特点,表明系统出现广义随机共振.特别地,分数阶与时滞的协同作用可能诱导随机共振的多样化.这就为在一定范围内调控随机共振提供了可能.展开更多
For an over-damped linear system subjected to both parametric excitation of colored noise and external excitation of periodically modulated noise, and in the case that the cross-correlation intensity between noises is...For an over-damped linear system subjected to both parametric excitation of colored noise and external excitation of periodically modulated noise, and in the case that the cross-correlation intensity between noises is a time-periodic function, we study the stochastic resonance （SR） in this paper. Using the Shapiro-Loginov formula, we acquire the exact expressions of the first-order and the second-order moments. By the stochastic averaging method, we obtain the analytical expression of the output signal-to-noise ratio （SNR）. Meanwhile, we discuss the evolutions of the SNR with the signal frequency, noise intensity, correlation rate of noise, time period, and modulation frequency. We find a new bona fide SR. The evolution of the SNR with the signal frequency presents periodic oscillation, which is not observed in a conventional linear system. We obtain the conventional SR of the SNR with the noise intensity and the correlation rate of noise. We also obtain the SR in a wide sense, in which the evolution of the SNR with time period modulation frequency presents periodic oscillation. We find that the time-periodic modulation of the cross-correlation intensity between noises diversifies the stochastic resonance phenomena and makes this system possess richer dynamic behaviors.展开更多
文摘本文研究了含信号调制噪声和频率波动的小时滞线性分数阶振子的随机共振.利用分数阶Shapiro-Loginov公式和Laplace变换技巧,本文首先推导了系统响应的一阶稳态矩和稳态响应振幅增益(Output Amplitude Gain, OAG)的解析表达式,然后讨论了分数阶、时滞和噪声参数对OAG的影响.结果显示:各参数对OAG的影响均呈现非单调变化的特点,表明系统出现广义随机共振.特别地,分数阶与时滞的协同作用可能诱导随机共振的多样化.这就为在一定范围内调控随机共振提供了可能.
基金Project supported by the National Natural Science Foundation of China(Grant No.11171238)the Young Teacher Fund of Fujian Agriculture and Forestry Uninversity,China(Grant No.2011XJJ23)the Science and Technology Project of the Education Department of Sichuan Province,China(Grant No.14ZA0050)
文摘For an over-damped linear system subjected to both parametric excitation of colored noise and external excitation of periodically modulated noise, and in the case that the cross-correlation intensity between noises is a time-periodic function, we study the stochastic resonance （SR） in this paper. Using the Shapiro-Loginov formula, we acquire the exact expressions of the first-order and the second-order moments. By the stochastic averaging method, we obtain the analytical expression of the output signal-to-noise ratio （SNR）. Meanwhile, we discuss the evolutions of the SNR with the signal frequency, noise intensity, correlation rate of noise, time period, and modulation frequency. We find a new bona fide SR. The evolution of the SNR with the signal frequency presents periodic oscillation, which is not observed in a conventional linear system. We obtain the conventional SR of the SNR with the noise intensity and the correlation rate of noise. We also obtain the SR in a wide sense, in which the evolution of the SNR with time period modulation frequency presents periodic oscillation. We find that the time-periodic modulation of the cross-correlation intensity between noises diversifies the stochastic resonance phenomena and makes this system possess richer dynamic behaviors.
