双值噪声扰动下分数阶串联电路的随机共振现象

本文研究由被双态噪声调制的电阻、被双态噪声调制的周期输入信号以及通过分数阶微分方程描述的容阻器串联组成的简单电路的随机共振特性. 首先, 利用整数阶微分方程Shapiro- Loginov公式以及广义分数阶微分方程Shapiro-Loginov公式, 得到一组封闭的方程组; 其次, 对封闭方程组利用Laplace变换、逆Laplace变换, 推导出用分数阶微分方程描述的系统一阶矩以及稳态时响应振幅的详细表达式; 再次, 通过Matlab模拟, 根据稳态时响应振幅的表达式, 画出稳态时振幅随系统阶数、周期信号频率、双态噪声强度、双态噪声关联时间的变化图. 从图中发现系统表现出2种不同的随机共振现象—–Bona fide随机共振现象以及广义的随机共振现象.

Stochastic resonance caused by the dichotomous noise in a fractional order series circuit

The characteristics of the stochastic resonance of the series circuits composed of the modulated- resistance with the symmetrical dichotomous noise, and the modulated-amplitude with the symmetrical dichotomous noise and the fractional-order cap-resistor is investigated. Firstly, by applying the interger-order Shapiro-Loginov formula and the fractional-order Shapiro-Loginov formula, a set of closed equations are obtained; Secondly, using the Laplace transform technique, the inverse Laplace transform technique and “signal and system” theory, the steady state analytic expression of the first moment of the amplitude of the output signal is derived; Lastly, by simulating the variation of the driving frequency, the fractional-order cap-resistor is fomulated. For the noise parameters in terms of the steady state amplitude of the output signal, the non-monotonic behavior of the output signal is identified. The result indicates that the Bona fide stochastic resonance and the generalized stochastic resonance phenomena occur in the fractional-order series circuits.