一类含分布时滞革新传播模型的稳定性  

The Stability of an Innovation Diffusion Model with Delay

作　　者：赵宏伟[1] 焉波[1] 

机构地区：[1]北华大学数学学院,吉林吉林132021

出　　处：《生物数学学报》2008年第1期107-115,共9页Journal of Biomathematics

摘　　要：建立了一类含分布时滞的革新传播模型(dU(t))/(dt)=-(α+βA(t))U(t)-ρU(t)+ρ,(dA(t))/(dt)=integral from 0 to (+∞)αE(τ)U(t-τ)dr+βu(t)A(t)-(ρ+κ)A(t).研究了分布时滞对传播过程的影响,讨论了正平衡点的存在性和唯一性及其局部与全局的渐近稳定性.当分布时滞的核函数取δe^(-δτ)时,证明了正平衡点是绝对渐近稳定的.In this paper, an innovation diffusion model with distributed time delay is proposed and its effect on the diffusion process is studied. The existence and uniqueness of a positive equilibrium is proven and the sufl：icient conditions for its locally and globally asymptotic stability are obtained. When the kernel function of the distributed time delay takes the form δe^-δτ, it is proved that the positive equilibrium is absolutely asymptotically stable.

关 键 词：革新传播模型 分布时滞 正平衡点 渐近稳定性 

分 类 号：O175.3[理学—数学]