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.
出处
《生物数学学报》
CSCD
北大核心
2008年第1期107-115,共9页
Journal of Biomathematics
关键词
革新传播模型
分布时滞
正平衡点
渐近稳定性
Innovation diffusion model
Distributed time delay
Positive equilibrium
Asymptotic stability
