【摘要】 研究了具有功能性反应函数（x^α）/(1+βx^α+ωx^2α)捕食者—食饵系统的定性行为.在这个系统中,当无捕食者时,食饵密度按照函数x（a-bx^α）变化.通过对系统的分析和构造李雅谱诺夫函数,分别得出在适当条件下系统非负平衡点的局部稳定性和全局稳定性,以及当正平衡不稳定时,系统在参数变化范围内存在唯一稳定的极限环.更多还原

【Abstract】 Qualitative behavior for predator-prey systems with the functional response（x^α）/(1+βx^α+ωx^2α) was studied.In this system,the prey density changed with the function x（a-bx^α）when there was not a predator.Through theoretical analysis and structuring Liapunov function,it was concluded that the system is partially stable or globally stable in suitable conditions and has a unique stable limit cycle within the change of the parameters if the positive equilibrium point is unstable.更多还原