This paper deals with a Lotka-Volterra ecological competition system with cubic functional responses and diffusion. We consider the stability of semitrivial solutions by using spectrum analysis. Taking the growth rate...This paper deals with a Lotka-Volterra ecological competition system with cubic functional responses and diffusion. We consider the stability of semitrivial solutions by using spectrum analysis. Taking the growth rate as a bifurcation parameter and using the bifurcation theory, we discuss the existence and stability of the bifurcating solutions which emanate from the semi-trivial solutions.展开更多
The present paper deals with a singular nonlinear boundary value problem arising in the theory of power law fluids, sufficient conditions for the existence of bifurcation solutions to the problem are obtained.
This paper investigates the dynamics of a TCP system described by a first- order nonlinear delay differential equation. By analyzing the associated characteristic transcendental equation, it is shown that a Hopf bifur...This paper investigates the dynamics of a TCP system described by a first- order nonlinear delay differential equation. By analyzing the associated characteristic transcendental equation, it is shown that a Hopf bifurcation sequence occurs at the pos- itive equilibrium as the delay passes through a sequence of critical values. The explicit algorithms for determining the Hopf bifurcation direction and the stability of the bifur- cating periodic solutions are derived with the normal form theory and the center manifold theory. The global existence of periodic solutions is also established with the method of Wu （Wu, J. H. Symmetric functional differential equations and neural networks with memory. Transactions of the American Mathematical Society 350（12）, 4799-4838 （1998））.展开更多
In this paper, based on the generalized variational principle of plates, the buckled states of rectangular plates under uniaxial compression are studied by use of the finite element method and the numerical analysis r...In this paper, based on the generalized variational principle of plates, the buckled states of rectangular plates under uniaxial compression are studied by use of the finite element method and the numerical analysis results under various boundary conditions are obtained by using the continuation calculation method.展开更多
On the basis of von Karnmnequations, the axisymmetric buckling and post-buckling of annular plates on anelastic foundation is so wematically discussed byusing shooting
Nonlinear solution of reinforced concrete structures, particularly complete load-deflection response, requires tracing of the equilibrium path and proper treatment of the limit and bifurcation points. In this regard, ...Nonlinear solution of reinforced concrete structures, particularly complete load-deflection response, requires tracing of the equilibrium path and proper treatment of the limit and bifurcation points. In this regard, ordinary solution techniques lead to instability near the limit points and also have problems in case of snap-through and snap-back. Thus they fail to predict the complete load-displacement response. The arc-length method serves the purpose well in principle, received wide acceptance in finite element analysis, and has been used extensively. However modifications to the basic idea are vital to meet the particular needs of the analysis. This paper reviews some of the recent developments of the method in the last two decades, with particular emphasis on nonlinear finite element analysis of reinforced concrete structures.展开更多
Based on non-equilibrium thermodynamic theory, a temperature field model of gun muzzle is setup We obtain not only a solitary solution, but also a bifurcation solution. The physical picture of the solutions is corresp...Based on non-equilibrium thermodynamic theory, a temperature field model of gun muzzle is setup We obtain not only a solitary solution, but also a bifurcation solution. The physical picture of the solutions is corresponding to the center flame and secondary flame of the gun muzzle.展开更多
The quasi-periodic perturbation for the Duffing's equation with two external forcing terms has been discussed. The second order averaging method and sub-harmonic Melnikov's method through the medium of the ave...The quasi-periodic perturbation for the Duffing's equation with two external forcing terms has been discussed. The second order averaging method and sub-harmonic Melnikov's method through the medium of the averaging mrthod have been applied to detect the existence of quasiperiodic solutions and sub-harmonic bifurcation for the system. Sub-harmonic bifurcation curves are given by using numerical computation for sub-harmonic Melnikov's function.展开更多
In this paper,a system of reaction-diffusion equations arising in a nutrient-phytoplankton populations is investigated.The equations model a situation in which phytoplankton population is divided into two groups,namel...In this paper,a system of reaction-diffusion equations arising in a nutrient-phytoplankton populations is investigated.The equations model a situation in which phytoplankton population is divided into two groups,namely susceptible phytoplankton and infected phytoplankton.A number of existence and non-existence results about the non-constant steady states of a reaction diffusion system are given.If the diffusion coefficient of the infected phytoplankton is treated as bifurcation parameter,non-constant positive steady-state solutions may bifurcate from the constant steady-state solution under some conditions.展开更多
基金supported partly by the NSF (10971124,11001160) of ChinaNSC (972628-M-110-003-MY3) (Taiwan)the Fundamental Research Funds (GK201002046) for the Central Universities
文摘This paper deals with a Lotka-Volterra ecological competition system with cubic functional responses and diffusion. We consider the stability of semitrivial solutions by using spectrum analysis. Taking the growth rate as a bifurcation parameter and using the bifurcation theory, we discuss the existence and stability of the bifurcating solutions which emanate from the semi-trivial solutions.
文摘The present paper deals with a singular nonlinear boundary value problem arising in the theory of power law fluids, sufficient conditions for the existence of bifurcation solutions to the problem are obtained.
基金Project supported by the National Natural Science Foundation of China (Nos. 10771215 and10771094)
文摘This paper investigates the dynamics of a TCP system described by a first- order nonlinear delay differential equation. By analyzing the associated characteristic transcendental equation, it is shown that a Hopf bifurcation sequence occurs at the pos- itive equilibrium as the delay passes through a sequence of critical values. The explicit algorithms for determining the Hopf bifurcation direction and the stability of the bifur- cating periodic solutions are derived with the normal form theory and the center manifold theory. The global existence of periodic solutions is also established with the method of Wu （Wu, J. H. Symmetric functional differential equations and neural networks with memory. Transactions of the American Mathematical Society 350（12）, 4799-4838 （1998））.
基金The project supported by Gansu Province Natural Science Foundation
文摘In this paper, based on the generalized variational principle of plates, the buckled states of rectangular plates under uniaxial compression are studied by use of the finite element method and the numerical analysis results under various boundary conditions are obtained by using the continuation calculation method.
基金Project support by the State Education Commission of the People’s Republic of China
文摘On the basis of von Karnmnequations, the axisymmetric buckling and post-buckling of annular plates on anelastic foundation is so wematically discussed byusing shooting
文摘Nonlinear solution of reinforced concrete structures, particularly complete load-deflection response, requires tracing of the equilibrium path and proper treatment of the limit and bifurcation points. In this regard, ordinary solution techniques lead to instability near the limit points and also have problems in case of snap-through and snap-back. Thus they fail to predict the complete load-displacement response. The arc-length method serves the purpose well in principle, received wide acceptance in finite element analysis, and has been used extensively. However modifications to the basic idea are vital to meet the particular needs of the analysis. This paper reviews some of the recent developments of the method in the last two decades, with particular emphasis on nonlinear finite element analysis of reinforced concrete structures.
文摘Based on non-equilibrium thermodynamic theory, a temperature field model of gun muzzle is setup We obtain not only a solitary solution, but also a bifurcation solution. The physical picture of the solutions is corresponding to the center flame and secondary flame of the gun muzzle.
文摘The quasi-periodic perturbation for the Duffing's equation with two external forcing terms has been discussed. The second order averaging method and sub-harmonic Melnikov's method through the medium of the averaging mrthod have been applied to detect the existence of quasiperiodic solutions and sub-harmonic bifurcation for the system. Sub-harmonic bifurcation curves are given by using numerical computation for sub-harmonic Melnikov's function.
基金Supported by the National Natural Science Foundation of China(No.10771085)
文摘In this paper,a system of reaction-diffusion equations arising in a nutrient-phytoplankton populations is investigated.The equations model a situation in which phytoplankton population is divided into two groups,namely susceptible phytoplankton and infected phytoplankton.A number of existence and non-existence results about the non-constant steady states of a reaction diffusion system are given.If the diffusion coefficient of the infected phytoplankton is treated as bifurcation parameter,non-constant positive steady-state solutions may bifurcate from the constant steady-state solution under some conditions.
