一类带有扩散项的病毒模型的动态分歧

Dynamic Bifurcation of a Viral Dynamics Model with Diffusion Responses

本文利用线性全连续场谱理论,中心流形约化与非线性耗散系统吸引子分歧与跃迁理论研究了一类带有扩散项的病毒模型的动态分歧,该模型的分歧与区域Ω的选取有关,当∫_Ωψ_1~3dx≠0时,控制参数λ大于临界点时,方程从平衡态处发生分歧,原有的平衡态失稳,分歧出一个稳定的奇点吸引子,在λ小于临界点一侧分歧出唯一的鞍点;当∫_Ωψ_1~3dx=0时,本文给出了上述模型发生分歧的条件及临界点,当λ大于临界点,原有平衡态失稳,方程从平衡态处发生分歧,分歧出两个稳定奇点,当λ小于临界点时,方程从平衡态处分歧出两个鞍点.本文给出了在Dirichlet边界条件下,方程分歧出的稳定奇点吸引子和两个鞍点的表达式.

With the guidance of spectrum theory of the linear completelycontinuous fields,center manifolds reduction method and transition theory of nonlinear dissipative system,this paper invests dynamic bifurcation of a class of viral dynamics model with diffusion term. The bifurcation of the model is associated with the region.Whenthe control parameteris greater than the critical point,the equation diverges a stable singular from the equilibrium state which becomes unstable,and the equation diverges one only saddle point as the control parameteris less than the critical point. This paper proposes the conditions of the divergence and its critical point： the equation diverges two stable singular points and two saddle points from the equilibrium state as the control parameteris greater than the critical pointand less than the critical point under some condition. The expression of the stable singular and two saddle points of the equation with Dirichlet boundary condition are given in this paper.