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
The canard explosion phenomenon in a predator-prey model with Michaelis-Menten functional response is analyzed in this paper by employing the geometric singular perturbation theory. First, some turning points, such as...The canard explosion phenomenon in a predator-prey model with Michaelis-Menten functional response is analyzed in this paper by employing the geometric singular perturbation theory. First, some turning points, such as, fold point, transcritical point, pitchfork point, canard point, are identified;then Hopf bifurcation, relaxation oscillation, together with the canard transition from Hopf bifurcation to relaxation oscillation are discussed.展开更多
Time-delay effects on synchronization features of delay-coupled slow-fast van der Pol systems are investigated in the present paper. The synchronization mechanism of “slow-manifold adjustment” is firstly described o...Time-delay effects on synchronization features of delay-coupled slow-fast van der Pol systems are investigated in the present paper. The synchronization mechanism of “slow-manifold adjustment” is firstly described on the basis of geometric singular perturbation theory. Then, the impact of time delay on the structure of the slow manifold of synchronized system is obtained by using the method of stability switch, and thus, time-delay effects on synchronization features are stated. It is shown the time delay cannot qualitatively affect the synchronization mechanism, however, it can result in the drift of the optimal coupling strength.展开更多
Van der Waals方程是一类重要的非线性偏微分方程,能够描述非弹性碰撞粒子流的动力学行为。本文证明了在充分小色散情况下,具有五阶色散项的Van der Waals方程波前解的持续存在性。首先,由于其波前解实际对应三维空间的异宿轨,利用辐角...Van der Waals方程是一类重要的非线性偏微分方程,能够描述非弹性碰撞粒子流的动力学行为。本文证明了在充分小色散情况下,具有五阶色散项的Van der Waals方程波前解的持续存在性。首先,由于其波前解实际对应三维空间的异宿轨,利用辐角原理计算了其平衡点的稳定和不稳定流形的维数。其次,由于三维空间异宿轨的存在性研究是一个困难的问题,利用几何奇异摄动理论证明慢系统的临界流形是法向双曲的,进而把三维问题转化为二维问题。最后,在未扰动系统存在异宿轨的情况下,利用隐函数定理证明扰动系统的稳定流形与不稳定流形横截相交,即异宿轨的持续存在性。展开更多
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.
文摘The canard explosion phenomenon in a predator-prey model with Michaelis-Menten functional response is analyzed in this paper by employing the geometric singular perturbation theory. First, some turning points, such as, fold point, transcritical point, pitchfork point, canard point, are identified;then Hopf bifurcation, relaxation oscillation, together with the canard transition from Hopf bifurcation to relaxation oscillation are discussed.
文摘Time-delay effects on synchronization features of delay-coupled slow-fast van der Pol systems are investigated in the present paper. The synchronization mechanism of “slow-manifold adjustment” is firstly described on the basis of geometric singular perturbation theory. Then, the impact of time delay on the structure of the slow manifold of synchronized system is obtained by using the method of stability switch, and thus, time-delay effects on synchronization features are stated. It is shown the time delay cannot qualitatively affect the synchronization mechanism, however, it can result in the drift of the optimal coupling strength.
文摘Van der Waals方程是一类重要的非线性偏微分方程,能够描述非弹性碰撞粒子流的动力学行为。本文证明了在充分小色散情况下,具有五阶色散项的Van der Waals方程波前解的持续存在性。首先,由于其波前解实际对应三维空间的异宿轨,利用辐角原理计算了其平衡点的稳定和不稳定流形的维数。其次,由于三维空间异宿轨的存在性研究是一个困难的问题,利用几何奇异摄动理论证明慢系统的临界流形是法向双曲的,进而把三维问题转化为二维问题。最后,在未扰动系统存在异宿轨的情况下,利用隐函数定理证明扰动系统的稳定流形与不稳定流形横截相交,即异宿轨的持续存在性。
