摘要
本文的主要工作是在食饵单种群满足S-型生长的广义Loqisric模型条件基础上,对具有功能性反应的食饵与捕食者两种群模型进行定性分析,研究了平衡点的性态及正平衡点的全局渐近稳定性并探讨了正平衡点外围极限环的情况.
Based on Chen Junping's paper in which the model was put forward as follows dx/dt=x(a-bx)-αx^2y/(x^2+β~2) dy/dt=-ey+kαx^2y/(x^2+β~2) but the linear part (a-bx) in the first equation was not applicable for the description of predator in most cases, this paper is to develop the linear part into the continuous generalized logistic model which describes the shaped growth of prey better.The new model is presented as follows dx/dt=rx(m-x)/(m+ux)-αx^2y/(x^2+β~2) dy/dt=-ey+kαx^2y/(x^2+β~2) where γ, m, α, β, k, e are all positive constants with ecological meanings and x, y represents the density of prey and predator respectively.Control variable u varies from-1 to 0, by which we can see all the possible cases of the ecological environment. The behaviour and the globally asymptotic stability of equilibrium points, the boundedness of the solutions and the existence of the limit cycles are studied, The ecological meanings of these conllusions have been interpreted.
出处
《华东师范大学学报（自然科学版）》
CAS
CSCD
1992年第3期15-20,共6页
Journal of East China Normal University(Natural Science)
关键词
功能性反应
食饵
捕食者
群模型
generalized logistic model functional responce
