In this paper,we investigate a two-dimensional avian influenza model with Allee effect and stochasticity.We first show that a unique global positive solution always exists to the stochastic system for any positive ini...In this paper,we investigate a two-dimensional avian influenza model with Allee effect and stochasticity.We first show that a unique global positive solution always exists to the stochastic system for any positive initial value.Then,under certain conditions,this solution is proved to be stochastically ultimately bounded.Furthermore,by constructing a suitable Lyapunov function,we obtain sufficient conditions for the existence of stationary distribution with ergodicity.The conditions for the extinction of infected avian population are also analytically studied.These theoretical results are conformed by computational simulations.We numerically show that the environmental noise can bring different dynamical outcomes to the stochastic model.By scanning different noise intensities,we observe that large noise can cause extinction of infected avian population,which suggests the repression of noise on the spread of avian virus.展开更多
The anti-periodic traveling wave solutions to a forced two-dimensional generalized KdV-Burgers equation are studied. Some theorems concerning the boundness, existence and uniqueness of the solution to this equation ar...The anti-periodic traveling wave solutions to a forced two-dimensional generalized KdV-Burgers equation are studied. Some theorems concerning the boundness, existence and uniqueness of the solution to this equation are proved.展开更多
讨论了方程L_nX(t)+sum from (j=0) to m b_j(t)f_j(X(t-τ_j(t)))=P(t)(其中L_n*=1/(P_n(t))d/(dt)1/(P_(n-1)(t)…d/(dt)1/(P_1(t))×d/(dt)*/(P_0(t)),0<τ_j(t)≤τ,j=0,…,m)解的渐近性质,给出了解有界及解趋于零的判定准则.
讨论了方程L_nX(T)+sum from j=0 to m( )b_j(t)f_j(X(t-τ_i(t)))=P(t)≠0(j=0,…m)时解的渐近性质,给出了解有界及解趋于零的判定准则(其中L_n*=1/P_n(t)d/dt1/P_(n-1)(t)…d/dt1/p_1(t)d/dt*/p_0(t))
基金This study is supported by the National Key Research and Development Program of China(2018YFA0801103)the National Natural Science Foundation of China(Grant No.12071330 to Ling Yang,Grant No.11701405 to Jie Yan).
文摘In this paper,we investigate a two-dimensional avian influenza model with Allee effect and stochasticity.We first show that a unique global positive solution always exists to the stochastic system for any positive initial value.Then,under certain conditions,this solution is proved to be stochastically ultimately bounded.Furthermore,by constructing a suitable Lyapunov function,we obtain sufficient conditions for the existence of stationary distribution with ergodicity.The conditions for the extinction of infected avian population are also analytically studied.These theoretical results are conformed by computational simulations.We numerically show that the environmental noise can bring different dynamical outcomes to the stochastic model.By scanning different noise intensities,we observe that large noise can cause extinction of infected avian population,which suggests the repression of noise on the spread of avian virus.
文摘The anti-periodic traveling wave solutions to a forced two-dimensional generalized KdV-Burgers equation are studied. Some theorems concerning the boundness, existence and uniqueness of the solution to this equation are proved.
文摘讨论了方程L_nX(t)+sum from (j=0) to m b_j(t)f_j(X(t-τ_j(t)))=P(t)(其中L_n*=1/(P_n(t))d/(dt)1/(P_(n-1)(t)…d/(dt)1/(P_1(t))×d/(dt)*/(P_0(t)),0<τ_j(t)≤τ,j=0,…,m)解的渐近性质,给出了解有界及解趋于零的判定准则.
文摘讨论了方程L_nX(T)+sum from j=0 to m( )b_j(t)f_j(X(t-τ_i(t)))=P(t)≠0(j=0,…m)时解的渐近性质,给出了解有界及解趋于零的判定准则(其中L_n*=1/P_n(t)d/dt1/P_(n-1)(t)…d/dt1/p_1(t)d/dt*/p_0(t))
