摘要
毒素影响种群的内禀增长率为非线性函数的三维捕食-食饵模型的研究已取得了较好的结果.在此基础上,以变系数非线性微分方程为基础建立一类三维捕食-食饵模型.该模型不仅考虑毒素影响种群的内禀增长率为非线性函数,还考虑毒素影响到种内和种间的作用系数.利用积分均值法,研究此模型的动力学性质,结果表明:在一定条件下3个种群均走向绝灭或均弱平均持续生存,得到各种群平均持续生存与绝灭的阈值,从而给出系统持续生存和绝灭的充分条件.
The three-dimensional predator-prey model that the intrinsic growth rate is a nonlinear function on the toxicant in the population has achieved good results.On the basis,a class of three-dimensional predator-prey model is established based on variable coefficient nonlinear differential equations.The model not only considers that the intrinsic growth rate is a nonlinear function on the toxicant in the population,but also considers the toxins effect on intraspecific and interspecific interaction coefficient.By using the method of integral average,we study the dynamical properties of the model.Research shows the three populations are going extinct or permanent in the mean under certain conditions.The thresholds of permanence in mean and extinction for each species are obtained.Thus we give sufficient condition for the permanence and extinction of the system.
出处
《沈阳化工大学学报》
CAS
2012年第4期373-376,共4页
Journal of Shenyang University of Chemical Technology
关键词
污染环境
捕食-食饵模型
持续生存
绝灭
阈值
polluted environment
predator-prey model
permanence
extinction
threshold
