摘要
建立了可以描述自然生物生存环境复杂度的捕食生态系统的随机模型,并基于实验得到的系统参数研究了生存环境复杂程度和随机激励强度对两个物种的稳态概率分布,以及系统由非临界状态到临界状态的平均首次穿越时间的影响.在弱扰动假设下应用Stratonovich-Khasminskii随机平均原理分别得到了两个物种的稳态概率密度函数并采用Monte-Carlo对原系统模拟来验证理论求解的正确性.利用Pontryagin方程得到了系统由非临界状态到临界状态的平均首次穿越时间表达式.研究表明:1)生存环境越简单的生态系统越容易受到随机因素的影响;2)随机干扰强度越大生态系统越不稳定;3)系统的平均首次穿越时间随生存环境复杂度提高而变长;4)作用在食物自然生长率的随机激励对系统的平均首次穿越时间影响较大.
To explore the habitat complexity and random environmental factors effects to the ecosystem,a new stochastic predation type ecosystem with habitat complexity was proposed.Both theoretical analysis and numerical analysis were explored.With the assumption of weak disturbances,the stationary probability density functions（PDF） for both species were obtained by applying the StratonovichKhasminskii averaging principle.The accuracy of the results obtained from theoretical method was demonstrated by those obtained from Monte Carlo simulation（MCS）.The system mean first passage time（MFPT） was solved from the Pontryagin equation.The effects of the habitat complexity and the noise intensity were investigated via numerical calculations based on the data obtained from experiment.Results obtained show that： 1） the ecosystem with smaller habitat complexity is less stable when the system is disturbed by noises;2） the stronger the noise intensities are,the less stable the ecosystem will be;3） the ecosystem with bigger habitat complexity has longer MFPT;4） the noise added to the prey natural increase rate has a bigger effect on the MFPT than that added to the predator natural death rate does.
出处
《应用数学和力学》
CSCD
北大核心
2013年第2期162-171,共10页
Applied Mathematics and Mechanics
基金
国家自然基金资助项目(11172233
0932009
61171155)
陕西省自然科学基金资助项目(2012JM8010)
