Influences of prey refuge on the dynamics of a predator-prey model with ratio-dependent functional response are investigated. The local and global stability of positive equilibrium of the system are considered. Theore...Influences of prey refuge on the dynamics of a predator-prey model with ratio-dependent functional response are investigated. The local and global stability of positive equilibrium of the system are considered. Theoretical analysis indicates that constant refuge leads to the system undergo supercritical Hopf bifurcation twice with the birth rate of prey species changing continuously.展开更多
In this paper,we present two-level defect-correction finite element method for steady Navier-Stokes equations at high Reynolds number with the friction boundary conditions,which results in a variational inequality pro...In this paper,we present two-level defect-correction finite element method for steady Navier-Stokes equations at high Reynolds number with the friction boundary conditions,which results in a variational inequality problem of the second kind.Based on Taylor-Hood element,we solve a variational inequality problem of Navier-Stokes type on the coarse mesh and solve a variational inequality problem of Navier-Stokes type corresponding to Newton linearization on the fine mesh.The error estimates for the velocity in the H1 norm and the pressure in the L^(2) norm are derived.Finally,the numerical results are provided to confirm our theoretical analysis.展开更多
基金Supported by the NNSF of China(11126284)Supported by the NSF of Department of Education of Henan Province(12A110012)Supported by the Young Scientific Research Foundation of Henan Normal University(1001)
文摘Influences of prey refuge on the dynamics of a predator-prey model with ratio-dependent functional response are investigated. The local and global stability of positive equilibrium of the system are considered. Theoretical analysis indicates that constant refuge leads to the system undergo supercritical Hopf bifurcation twice with the birth rate of prey species changing continuously.
基金supported by Zhejiang Provincial Natural Science Foundation with Grant Nos.LY12A01015,LY14A010020 and LY16A010017.
文摘In this paper,we present two-level defect-correction finite element method for steady Navier-Stokes equations at high Reynolds number with the friction boundary conditions,which results in a variational inequality problem of the second kind.Based on Taylor-Hood element,we solve a variational inequality problem of Navier-Stokes type on the coarse mesh and solve a variational inequality problem of Navier-Stokes type corresponding to Newton linearization on the fine mesh.The error estimates for the velocity in the H1 norm and the pressure in the L^(2) norm are derived.Finally,the numerical results are provided to confirm our theoretical analysis.
