实部与虚部关联复噪声诱导的激光系统的广义随机共振研究

Stochastic resonance is one of preceding issues in nonlinear science. And lasers have wide range of applications in many various fields. Recently, the most research is focused on the stochastic resonance in Langevin equation with real noise. Few papers studied the stochastic resonance in laser systems driven by complex noise. The stochastic resonance in laser systems induced by complex noise with cross-correlation between the real part and imaginary part requires further research and improvement. The project is expected to study the stochastic resonance of bistable optical systems with periodic signal modulation combined with multiplicative noise and additive noise. The project is expected to study the stochastic resonance in rotating wave Van der Pol oscillator induced by complex noise with cross-correlation between the real part and imaginary part. The project is expected to study the stochastic resonance in laser systems with the saturable absorption driven by additive complex noise and multiplicative complex noise. The project will study the stochastic resonance in semiconductor laser systems with additive complex noise and multiplicative complex noise. The project is expected to study the stationary probability distribution by using the Novikov theorem, the unified colored noise approximation and the Fokker-Planck equation. Then the project will obtain the exact expressions of indicators of stochastic resonance. Furthermore, the project will study the generalized stochastic resonance, stochastic multiresonace and the other phenomenon of stochastic resonance. The investigation of this project will not only enrich the research ideas of theory of stochastic resonance, but also provide the potential applications of laser model systems.

随机共振是非线性科学若干前沿问题之一，并且激光在各个领域都有重要的应用。目前已有研究主要集中于实噪声激励的朗之万方程的随机共振，少许文献研究激光系统受复噪声激励的随机共振。实部与虚部关联复噪声诱导的激光系统的广义随机共振需要进一步研究和完善。项目拟研究受输入光周期调制且受乘性噪声与加性噪声互相关激励的双稳光学系统的随机共振；拟研究实部与虚部关联复噪声激诱导的旋转波Van der Pol振子的随机共振；拟研究受加性复噪声与乘性复噪声激励的可饱和吸收的激光系统的随机共振；拟研究受加性复噪声与乘性复噪声激励的半导体激光系统的随机共振。项目拟利用Novikov定理、统一色噪声近似法和Fokker-Planck方程得出稳态概率分布,进而得出衡量随机共振指标的解析表达式，并进一步研究广义随机共振现象，随机多共振等现象。项目的研究既可拓展随机共振理论的研究思路,又为激光模型的潜在应用提供理论依据。

随机共振是非线性科学若干前沿问题之一，并且激光在各个领域都有重要的应用。研究了受加性互相关量子噪声激励的旋转波Van der Pol振子的随机共振现象；研究了受加性噪声与乘性噪声激励的半导体激光系统的随机共振现象；得到几个常见激光场系统的随机共振机制；研究了噪声的实部与虚部的相关性对激光场强的影响；研究了带电粒子受均匀电场，均匀磁场(磁场方向与电场方向垂直)以及内置分数阶噪声影响的三维广义郎之万方程的输运模型与随机共振现象；研究了非线性乘性噪声作用下具有双分数阶阻尼的振子的随机共振现象；研究了随机Deffuant-Weisbuch模型在噪声强度与模型参数下的鲁棒共识性。得到二值噪声与高斯白噪声对激光系统的随机共振影响的关系。并研究了噪声的特征数和系统参数对激光统计性质和随机共振的影响。研究了分数阶噪声与乘性噪声对输出谱增益以及信噪比的随机共振影响；研究了随机共振出现的参数范围。项目的研究既拓展随机共振理论的研究思路,又为激光模型的潜在应用提供理论依据。