The existence and stability ol periodic solutions for the two-dimensional system x' = f(x)+?g(x ,a), 0<ε<<1 ,a?R whose unperturbed systemis Hamiltonian can be decided by using the signs of Melnikov's...The existence and stability ol periodic solutions for the two-dimensional system x' = f(x)+?g(x ,a), 0<ε<<1 ,a?R whose unperturbed systemis Hamiltonian can be decided by using the signs of Melnikov's function. The results can be applied to the construction of phase portraits in the bifurcation set of codimension two bifurcations of flows with doublezero eigenvalues.展开更多
In this paper, the cusp shaped wave pattern (Legeckis wave) along the Equatorial Front (EF) is modeled by a meandering jet, and the motion of fluid parcels in a two dimensional kinematic model of the meandering jet al...In this paper, the cusp shaped wave pattern (Legeckis wave) along the Equatorial Front (EF) is modeled by a meandering jet, and the motion of fluid parcels in a two dimensional kinematic model of the meandering jet along EF is studied using Melnikov’s method. Results indicated that the velocity field of the cusp shaped wave pattern can indeed be modeled by a meandering jet; that the EF will act as a barrier to fluid exchange if there is no variability, but that it is just the variability that moves the buoy across the EF.展开更多
Dynamical behavior of nonlinear oscillator under combined parametric and forcing excitation, which includes yon der Pol damping, is very complex. In this paper, Melnikov's method is used to study the heteroclinic ...Dynamical behavior of nonlinear oscillator under combined parametric and forcing excitation, which includes yon der Pol damping, is very complex. In this paper, Melnikov's method is used to study the heteroclinic orbit bifurcations, subharmonic bifurcations and chaos in this system. Smale horseshoes and chaotic motions can occur from odd subharmonic bifurcation of infinite order in this system-far various resonant cases finally the numerical computing method is used to study chaotic motions of this system. The results achieved reveal some new phenomena.展开更多
Chaotic attitude motion of a magnetic rigid spacecraft in a circular orbit of the earth is treated. The dynamical model of the problem was derived from the law of moment of momentum. The Melnikov analysis was carried ...Chaotic attitude motion of a magnetic rigid spacecraft in a circular orbit of the earth is treated. The dynamical model of the problem was derived from the law of moment of momentum. The Melnikov analysis was carried out to prove the existence of a complicated nonwandering Cantor set. The dynamical behaviors were numerically investigated by means of time history, Poincar map, power spectrum and Liapunov exponents. Numerical simulations indicate that the onset of chaos is characterized by break of torus as the increase of the torque of the magnetic forces.展开更多
The truncation equation for the derivative nonlinear Schrodinger equation has been dis- cussed in this paper. The existence of a special heteroclinic orbit has been found by using geometrical singular perturbation the...The truncation equation for the derivative nonlinear Schrodinger equation has been dis- cussed in this paper. The existence of a special heteroclinic orbit has been found by using geometrical singular perturbation theory together with Melnikov's technique.展开更多
基金The project is supported by the National Natural Science Foundation of China
文摘The existence and stability ol periodic solutions for the two-dimensional system x' = f(x)+?g(x ,a), 0<ε<<1 ,a?R whose unperturbed systemis Hamiltonian can be decided by using the signs of Melnikov's function. The results can be applied to the construction of phase portraits in the bifurcation set of codimension two bifurcations of flows with doublezero eigenvalues.
文摘In this paper, the cusp shaped wave pattern (Legeckis wave) along the Equatorial Front (EF) is modeled by a meandering jet, and the motion of fluid parcels in a two dimensional kinematic model of the meandering jet along EF is studied using Melnikov’s method. Results indicated that the velocity field of the cusp shaped wave pattern can indeed be modeled by a meandering jet; that the EF will act as a barrier to fluid exchange if there is no variability, but that it is just the variability that moves the buoy across the EF.
文摘Dynamical behavior of nonlinear oscillator under combined parametric and forcing excitation, which includes yon der Pol damping, is very complex. In this paper, Melnikov's method is used to study the heteroclinic orbit bifurcations, subharmonic bifurcations and chaos in this system. Smale horseshoes and chaotic motions can occur from odd subharmonic bifurcation of infinite order in this system-far various resonant cases finally the numerical computing method is used to study chaotic motions of this system. The results achieved reveal some new phenomena.
文摘Chaotic attitude motion of a magnetic rigid spacecraft in a circular orbit of the earth is treated. The dynamical model of the problem was derived from the law of moment of momentum. The Melnikov analysis was carried out to prove the existence of a complicated nonwandering Cantor set. The dynamical behaviors were numerically investigated by means of time history, Poincar map, power spectrum and Liapunov exponents. Numerical simulations indicate that the onset of chaos is characterized by break of torus as the increase of the torque of the magnetic forces.
文摘The truncation equation for the derivative nonlinear Schrodinger equation has been dis- cussed in this paper. The existence of a special heteroclinic orbit has been found by using geometrical singular perturbation theory together with Melnikov's technique.
