This paper discusses the existence and stability of steady-states for a three-dimensional system ef parabolic partial differential equations subject to Dirichlet boundary conditions, i.e. the situation in which a pred...This paper discusses the existence and stability of steady-states for a three-dimensional system ef parabolic partial differential equations subject to Dirichlet boundary conditions, i.e. the situation in which a predator feeds on twoprey species. Resultts are obtained by the use of spectral analysis and bifurcation theory.展开更多
In this paper, the existence and uniqueness of global solution of initial boundary value problem of degenerate competition diffusion system are proved by taking into account the quasimonotone of the nonlinear terms in...In this paper, the existence and uniqueness of global solution of initial boundary value problem of degenerate competition diffusion system are proved by taking into account the quasimonotone of the nonlinear terms in this system.展开更多
In this paper the influence of diffusion for stability of the prey-predator system with delay is studied. We analysed the conditions which raise the Hopf bifurcation. The problem is reduced by centralmanifold, and the...In this paper the influence of diffusion for stability of the prey-predator system with delay is studied. We analysed the conditions which raise the Hopf bifurcation. The problem is reduced by centralmanifold, and the approximation form of the stability periodic is obtained.展开更多
One predator two prey system is a research topic which has both the theoretical and practical values. This paper provides a natural condition of the existence of stable positive steady-state solutions for the one pred...One predator two prey system is a research topic which has both the theoretical and practical values. This paper provides a natural condition of the existence of stable positive steady-state solutions for the one predator two prey system. Under this condition we study the existence of the positive steady-state solutions at vicinity of the triple eigenvalue by implicit function theorem, discuss the positive stable solution problem bifurcated from the semi-trivial solutions containing two positive components with the help of bifurcation and perturbation methods.展开更多
文摘This paper discusses the existence and stability of steady-states for a three-dimensional system ef parabolic partial differential equations subject to Dirichlet boundary conditions, i.e. the situation in which a predator feeds on twoprey species. Resultts are obtained by the use of spectral analysis and bifurcation theory.
文摘In this paper, the existence and uniqueness of global solution of initial boundary value problem of degenerate competition diffusion system are proved by taking into account the quasimonotone of the nonlinear terms in this system.
基金This work is supported by National Science Foundatiin.
文摘In this paper the influence of diffusion for stability of the prey-predator system with delay is studied. We analysed the conditions which raise the Hopf bifurcation. The problem is reduced by centralmanifold, and the approximation form of the stability periodic is obtained.
基金This work is supported by National Science Foundation of China and the Fundes of Institute of Math (opened) Academic Sinica.
文摘One predator two prey system is a research topic which has both the theoretical and practical values. This paper provides a natural condition of the existence of stable positive steady-state solutions for the one predator two prey system. Under this condition we study the existence of the positive steady-state solutions at vicinity of the triple eigenvalue by implicit function theorem, discuss the positive stable solution problem bifurcated from the semi-trivial solutions containing two positive components with the help of bifurcation and perturbation methods.
