一个含有分布时滞的传播模型的稳定性

The Stability of a Diffusion Model with Distributed Time Delay

建立一个含有分布时滞的革新传播模型{U（t）=-αU（t）-ρU（t）＋ρ,A（t）=∫^＋∞ 0 αE（τ）U（t-τ）dτ-ρA（t）-kA（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惟一性及其渐近稳定性.当分布时滞的核函数取δe-^δt时,证明了正平衡点是绝对渐近稳定的.

An innovation diffusion model with distributed time delay is proposed {U（t）=-αU（t）-ρU（t）＋ρ,A（t）=∫^＋∞ 0 αE（τ）U（t-τ）dτ-ρA（t）-kA（t）. and its effect on the diffusion process is studied. The existence and uniqueness of a positive equilibrium is proven and the sufficient conditions for its asymptotic stability have been obtained. When the kernel function of the distributed time delay takes δe-^δt , the positive equilibrium is absolutely asymptotically stable.