摘要
基于关联噪声作用下的集合种群模型，通过理论计算与数值模拟方法，系统分析了噪声强度、交叉关联强度、噪声关联时间对稳态概率分布函数和平均首次通过时间曲线的影响。研究结果表明：（1）系统稳态概率分布函数的曲线呈现单峰结构，噪声强度和交叉关联强度的变化对稳态概率分布函数的结构有较大影响。（2）平均首次通过时间随噪声关联时间与交叉关联强度的影响呈现出相同的变化趋势。（3）平均首次通过时间作为交叉关联强度的函数时，噪声强度的变化会导致其出现较为剧烈的波动。平均首次通过时间作为噪声关联时间的函数，随着交叉关联强度的变化会出现特定阈值。上述研究结果有助于研究不同条件对种群系统稳定性的影响，不仅能通过更明确的方式来调节不同物种间的稳态关系，而且能为探索物种的变化规律提供理论依据，对种群的恢复和防治有一定指导意义。
关键词： 关联噪声；种群分布函数；首通时间；Fokker-Planck方程；统计性质
Abstract
Based on the metapopulation model under the influence of correlated noise, the effects of noise intensity, cross-correlation intensity and noise correlation time on the steady-state probability distribution function and the mean first passage time curve are systematically analyzed by theoretical calculation and numerical simulation. The results show that the curve of the steady-state probability distribution function of the system presents a single peak structure, and the changes of noise intensity and cross-correlation intensity have great influence on the structure of the steady-state probability distribution function. The mean first passage time shows the same trend with the influence of noise correlation time and cross correlation intensity. When the mean first passage time is a function of the cross-correlation intensity, the change of the noise intensity will lead to violent fluctuation. As the function of noise correlation time, the mean first passage time appears a certain threshold with the change of cross-correlation intensity. Above results are helpful to study the influence of different conditions on the stability of population system, not only to adjust the steady-state relationship between different species in a more clear way, but also to provide theoretical basis for exploring the changing law of species, which has certain guiding significance for the restoration and prevention of population.
Key words： Correlated noise; Population distribution function; First-passage time; Fokker-Planck equation; Statistical properties
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