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乘性二次噪声驱动的线性过阻尼振子的随机共振
Stochastic resonance in an over-damped linear oscillator driven by multiplicative quadratic noise
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摘要: 针对乘性二次噪声和加性周期调制噪声联合驱动的线性过阻尼振子,利用随机平均法推导了系统响应的一阶、二阶稳态矩以及稳态响应振幅和方差的解析表达式.理论分析和仿真实验均表明这类系统具有比传统的由线性噪声驱动的线性系统更丰富的动力学特性;当二次噪声的系数满足一定条件时,系统稳态响应的振幅及方差均存在广义随机共振现象.Abstract: For an over-damped linear oscillator driven by mnltiplicative quadratic noise and periodic modulated noise, the exact analytical expressions of the first two moments, the amplitude and variance of the system steady-state response are obtained. We find that this system has richer dynamic behaviors than the traditional linear systems driven by linear noise; when the coefficients of the quadratic noise satisfy certain conditions, both the amplitude and the variance of the system steady-state response present stochastic resonance.
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