害虫、天敌和食料的数学模型

THE MATHEMATIC MODELS OF RELATIONSHIP AMONG PEST INSECT, NATURAL ENEMIES AND FEED ABOUNDANCE

本文从实际问题出发,结合已有的描述群落生态的数学模型,提出了一组描述马尾松毛虫(Dendrolimus pnnctalus,walker)、条毒蛾(Lymantria dissoluta,Swinhoe)、天敌和食料之间动态关系的数学模型: w(k+1=(a_1x(k+1)/(1+a_2x(k+1)/_z(k))+a_3w(k)/(1+a_4w(k)/y(k)) x(k+1)=b_1w(k)/(1+b_2w(k)/y(k))+b_3x(k)/(1+b_4x(k)/z(k))+ y(k+1)=c_1z(k)/[1+c_sz(k)+c_3y(k)][1+c_4w(k)+(k+1)] z(k+1)=d_1z(k)/[1+d_2z(k)][1+d_3x(k)+d_4w(k)] 对于这个模型的线性化形式,详细讨论了控制松毛虫的暴发所需的条件及其生态学机制。

In this paper, a set of model was developed to describe the relationship among Dendrolimus punctatus (w.) , Lymantria dissoluta (S.), natural enemies and feed aboundance based on a practical problem: w(k+1)=a_1x(k+1)/1+α_2x(k+1)/z(k)+α_3人(k)/1+α_4w(k)/y(k), x(k+1)=b_1w(k)/1+b_2w(k)/y(k)+b_3x(k)/1+b_4x(k)/z(k), y(k+1)=c_1y(k)/[1+c_2z(k)+C_3y(k)][1+c_4w(k)+c_5x(k+1)], z(k+1)=(d_1z(k))/([1+d_2z(k)][1+d_3x(k)+d_4w(k)]) In the meanwhile, these models were lincarized and the conditions required and ecological mechanism were detailly discussed fr controlling the D. punctatus.