全局耦合分数阶振子中非对称二分噪声和对称二分噪声诱导随机共振的比较研究
A comparative study of asymmetric dichotomous noise and symmetric trichotomous noise induced stochastic resonance in the globally coupled fractional oscillators
摘要：
集体行为，在随机共振方面，已被研究在全球耦合振荡器（分数阶的内部和外部阻尼），由正弦的力量，这是无噪声或噪声调制，并受到乘法二次非对称二分法或对称二分法噪声扰动的潜在参数，耦合因子和本地漂移力驱动。通过一个简单的模型，热浴和所施加的力之间的耦合的影响已经包括在内。的质量，摩擦和潜在的参数的变化对输出振幅增益作为噪声强度的函数的效果，已被细致地调查这两种类型的噪声和指数的依赖集体SR峰值振幅的振荡器参数已被确定和分析。在二阶非对称二分噪声的影响下，研究了势参数为零时系统粒子的直线运动的特殊情况，发现在外力频率很低的情况下，系统发生了随机共振.这就引出了非线性项在这种有色噪声中的重要性，这种现象是独一无二的。通过数值模拟验证了分析结果的准确性。
英文摘要：
The collective behaviour, in respect of stochastic resonance, has been studied in globally coupled oscillators (with fractional-order intrinsic and external damping), driven by a sinusoidal force which is either noise-free or noise-modulated, and subjected to multiplicative quadratic asymmetric dichotomous or symmetric trichotomous noise perturbing the potential parameter, the coupling factor and the local drift force. The influence of coupling between the heat bath and the applied force has been included through a simple model. The effect of variation in mass, friction and potential parameters on the output amplitude gains as function of noise-intensity, has been meticulously investigated for both types of noise and the exponents governing the dependence of collective SR peak amplitude on the three oscillator parameters have been determined and analysed. The special case arising from the zero value of the potential parameter, which implies rectilinear motion of the system particles in the absence of fluctuations, has been dealt with under the influence of the second-order asymmetric dichotomous noise and stochastic resonance has been found to occur at justifiably quite low frequencies of the external force. This brings out the importance of nonlinear term in this coloured noise, for which this phenomenon is unique. The accuracy of the analytical results has been substantiated through numerical simulations.
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