过阻尼分数阶Langevin方程及其随机共振  

Overdamped fractional Langevin equation and its stochastic resonance

作　　者：高仕龙[1,2] 钟苏川[1] 韦鹍[1] 马洪[1] 

机构地区：[1]四川大学数学学院,成都610064 [2]乐山师范学院数学与信息科学学院,乐山614000

出　　处：《物理学报》2012年第10期32-37,共6页Acta Physica Sinica

基　　金：国家自然科学基金重点项目(批准号:10731050);中国博士后科学基金(批准号:20100471651;201104693)资助的课题~~

摘　　要：通过对广义Langevin方程阻尼核函数的适当选取,在过阻尼的情形下,推导出分数阶Langevin方程.给合反常扩散理论和分数阶导数的记忆性,讨论了分数阶Langevin方程的物理意义,进而得出分数阶Langevin方程产生随机共振的内在机理.数值模拟表明,在一定的阶数范围内,分数阶Langevin方程可以产生随机共振,并且分数阶下的信噪比增益好于整数阶情形.By choosing an appropriate damping kernel function of generalized Langevin equation, fractional Langevin equation （FLE） is derived in the case of overdamped condition. With the theory of anomalous diffusion and the memory of fractional derivatives, the physical meaning of FLE is discussed. Moreover, the internal mechanism of stochastic resonance about FLE is obtained. Finally, the numerical simulation shows that in a certain range of the order, stochastic resonance appears in FLE, and it is evident that the SNR gain in fractional Langevin equation is better than that of the integer-order situation.

关 键 词：随机共振 分数阶Langevin方程 双稳系统 记忆性 

分 类 号：O411.1[理学—理论物理]