Levy噪声对振荡的抑制
Suppression of oscillations by Levy noise
摘要：
在定态非平衡情形下，得到了带有乘性Lévy噪声和任意力的随机方程对的解析解。这个解表明Lévy flights总是抑制与极限环有关的准周期运动。证明了Lévy噪声驱动的随机系统与Gauss噪声驱动的随机系统的区别在于，在$Δt\to 0$极限下，指数为$α<2$的Lévy变差$ΔL\sim(Δt)^{1/α}$远小于指数为$α<2$的Gauss变差$ΔW\sim(Δt)^{1/2}$.此外，这种差异表明，以消除微积分选择的问题，因为相关的除了物理力的顺序是$(Δt)^{2/α}\llΔt$。
英文摘要：
We find analytical solution of pair of stochastic equations with arbitrary forces and multiplicative Lévy noises in a steady-state nonequilibrium case. This solution shows that Lévy flights suppress always a quasi-periodical motion related to the limit cycle. We prove that difference between stochastic systems driven by Lévy and Gaussian noises is that the Lévy variation $ΔL\sim(Δt)^{1/α}$ with the exponent $α<2$ is much less than the Gaussian one $ΔW\sim(Δt)^{1/2}$ in the $Δt\to 0$ limit. Moreover, this difference is shown to remove the problem of the calculus choice because related addition to the physical force is of order $(Δt)^{2/α}\llΔt$.
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