反常扩散下周期驱动双稳态系统的随机共振
Stochastic resonance in periodically driven bistable systems subjected to anomalous diffusion
摘要：
随机共振的发生在双稳态系统进行异常扩散，这是由密度依赖的波动，重点研究了问题的分析公式，以及一个可能的分析推导的关键量词的随机共振。建立了描述系统动力学的非线性Fokker-Planck方程和相应的Ito-Langevin方程。在线性响应制度的频谱放大，信噪比和磁滞回线面积的解析表达式推导出量化的随机共振。发现这些量化器强烈依赖于控制扩散类型的参数，特别是表征信噪比的峰值仅出现在接近的参数范围内。结果表明，考虑反常扩散系统与周期信号的相互作用，可以更好地理解周期力驱动的双稳态系统中的随机共振现象.
英文摘要：
The occurrence of stochastic resonance in bistable systems undergoing anomalous diffusions, which arise from density-dependent fluctuations, is investigated with emphasis on the analytical formulation of the problem as well as a possible analytical derivation of key quantifiers of stochastic resonance. The nonlinear Fokker-Planck equation describing the system dynamics, together with the corresponding Ito-Langevin equation, are formulated. In the linear-response regime analytical expressions of the spectral amplification, of the signal-to-noise ratio and of the hysteresis loop area are derived as quantifiers of stochastic resonance. These quantifiers are found to be strongly dependent on the parameters controlling the type of diffusion, in particular the peak characterizing the signal-to-noise ratio occurs only in close ranges of parameters. Results introduce the relevant information that taking into consideration the interactions of anomalous diffusive systems with a periodic signal, can provide a better understanding of the physics of stochastic resonance in bistable systems driven by periodic forces.
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