噪声和生存环境对捕食生态系统的影响

徐伟; 戚鲁媛; 高维廷

doi:10.3879/j.issn.1000-0887.2013.02.006

噪声和生存环境对捕食生态系统的影响

doi: 10.3879/j.issn.1000-0887.2013.02.006

¹西北工业大学数学系,西安 710129;²西北工业大学电子信息学院,西安 710129

基金项目: 国家自然基金资助项目(11172233； 10932009； 61171155)；陕西省自然科学基金资助项目(2012JM8010)

详细信息

作者简介:
徐伟(1957—),男,西安人,教授,博士,博士生导师(通讯作者. E-mail: qiluyuan@gmail.com).

中图分类号: O316;TU351
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出版历程
- 收稿日期: 2012-12-17
- 修回日期: 2013-01-31
- 刊出日期: 2013-02-15

Effects of Noises and Habitat Complexity in the Prey-Predator Ecosystem

¹Department of Mathematics, Northwestern Polytechnical University,Xi’an 710129, P.R.China;²Department of Electronic Information, Northwestern Polytechnical University,Xi’an 710129, P.R.ChinaState Key Laboratory of Advanced Design and Manufacturing for Vehicle Body,Hunan University, Changsha 410082, P.R.China;²College of Mechanical and Vehicle Engineering, Hunan University,Changsha 410082, P.R.China

摘要

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．
- 随机生态系统 /
- 稳态概率密度 /
- 平均首次穿越时间 /
- 生存环境复杂
Abstract: 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 StratonovichKhasminskii 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.
- stochastic ecosystem /
- stationary probability density /
- mean first passage time /
- habitat complexity

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