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Truncation Analysis for the Derivative Schrodinger Equation

Acta Mathematica Sinica,English Series 2002年第1期18卷 137-146页

作者： XU Peng Cheng CHANG Qian Shun GUO Bo Ling Academy of Mathematics and System Sciences. Chinese Academy of Sciences. Beijing 100080. P. R. China Institute of Applied Physics and Computational Mathematics. P. O. Box 8009. Beijing 100080. P. R. China Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100080 P. R. China Institute of Applied Physics and Computational Mathematics 8009 Beijing 10080 P. R. China

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... 详细信息

关键词： Derivative nonlinear Schrodinger equation geometric singular perturbation theory Melnikov's technique

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Solitary Wave Solutions of Delayed Coupled Higgs Field Equation

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Acta Mathematica Sinica,English Series 2022年第1期38卷 97-106页

作者： Shu Guan JI Xiao Wan LI School of Mathematics and Statistics and Center for Mathematics and Interdisciplinary SciencesNortheast Normal UniversityChangchun 130024P.R.China School of Mathematics Jilin UniversityChangchun 130012P.R.China College of Mathematics and System Science Xinjiang UniversityUrumqi 830046P.R.China

This paper is devoted to the study of the solitary wave solutions for the delayed coupled Higgs field equation{vtt-uxx-αu+βf*u|u|^(2)-2uv-τu(|u|^(2))x=0 vtt+vxx-β(|u|^(x))xx=*** first establish the existence of solitary wave solutions for the corresponding equation without delay and perturbation by using the Hamiltonian system *** we consider the persistence of solitary wave solutions of the delayed coupled Higgs field equation by using the method of dynamical system,especially the geometric singular perturbation theory,invariant manifold theory and Fredholm *** to the relationship between solitary wave and homoclinic orbit,the coupled Higgs field equation is transformed into the ordinary differential equations with fast variables by using the variable *** is proved that the equations with perturbation also possess homoclinic orbit,and thus we obtain the existence of solitary wave solutions of the delayed coupled Higgs field equation.

关键词： delayed coupled Higgs field equation solitary wave solutions geometric singular perturbation theory Fredholm theory homoclinic orbit

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The Homoclinic Orbits in Nonlinear SchrdingerEquation

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Communications in Nonlinear Science and Numerical Simulation 1998年第3期 129-134页

作者： Pengcheng XU, Boling GUO and Qianshun CHANG(Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing 100080, China)(Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing100088, China)

The Persistence of Homoclinic orbits for perturbed nonlinear Schrodingerequation with five degree term under even periodic boundary conditions is *** existences of the homoclinic orbits for the truncation equation is ... 详细信息

关键词： nonlinear Schr■dinger equation geometric singular perturbation theory Melnikov’s analysis

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Canard Solutions in a Predator-Prey Model

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Journal of Applied Mathematics and Physics 2022年第5期10卷 1678-1693页

作者： Guojian Lin School of Mathematics Renmin University of China Beijing China

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.

关键词： Canard Explosion Relaxation Oscillation Predator-Prey Model geometric singular perturbation theory

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Time-Delay Effects on Synchronization of Coupled Slow-Fast Systems

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Journal of Applied Mathematics and Physics 2021年第4期9卷 635-647页

作者： Yuanguang Zheng Jianjian Zeng School of Mathematics and Information Science Nanchang Hangkong University Nanchang China

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.

关键词： Synchronization Slow-Fast System Time-Delay geometric singular perturbation theory

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The Mixed-mode Oscillations in Basic Bursting Model

The Mixed-mode Oscillations in Basic Bursting Model

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第二届全国神经动力学学术会议

作者： LU Bo LIU Shenquan LIU Xuanliang JIANG Xiaofang Department of Mathematics South China University of Technology

In this paper,we mainly discuss the mixed-mode oscillations in the basic bursting *** using the geometric singular perturbation theory the existence of MMO’s in the reduced basic bursting model is *** we give the numerical result on MMO’s,and we have observed the mixed-mode oscillations phenomenon and nonmixed-mode behavior in the ***,the influence of the parameters to the model is illustrated.

关键词： geometric singular perturbation theory Mixed-mode Oscillations Basic Bursting Model

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