一维 Frenkel－Kontorova 模型原子链的同宿轨和拟周期行为研究

doi:10.16854 /j.cnki.1000-0712.180230

大学物理 ›› 2018, Vol. 37 ›› Issue (12): 26-.doi: 10.16854 /j.cnki.1000-0712.180230

一维 Frenkel－Kontorova 模型原子链的同宿轨和拟周期行为研究

康举，黄头生，孟天祥，张化永

华北电力大学工程生态学与非线性科学研究中心，北京 102206

收稿日期:2018-04-16 接受日期:2018-06-16 出版日期:2018-12-20 发布日期:2019-01-17
通讯作者: 张化永，E-mail: rceens@ ncepu.edu.cn
作者简介:康举( 1992—) ，男，甘肃陇南人，华北电力大学工程生态学与非线性科学研究中心2016 级硕士研
基金资助:
水体污染控制与治理科技重大专项( 2017ZX07101- 002) ; 中央高校基本科研业务费专项资金( JB2017069) ; 国家自然科学基金
( 39560023) 资助

Study of homoclinic orbits and quasi-period behavior of atomic chain in the one-dimensional Frenkel-Kontorova model

KANG Ju，HUANG Tou-sheng，MENG Tian-xiang，ZHANG Hua-yong

Research Center for Engineering Ecology and Nonlinear Science，North China Electric Power University，Beijing 102206，China

Received:2018-04-16 Accepted:2018-06-16 Online:2018-12-20 Published:2019-01-17

摘要/Abstract

摘要： 基于一维Frenkel-Kontorova 模型，研究了原子链系统的同宿轨道、多周期振荡和拟周期振荡的动力学行为.首先，根

据Jacobian 矩阵的特征值判断了系统存在双曲型鞍焦点; 其次，运用Silnikov 定理判定了系统在鞍焦点处产生同宿轨道的条

件; 最后，通过数值模拟验证了系统存在同宿轨道、多周期振荡和拟周期振荡的动力学行为.本文的研究结果也为固体摩擦现

象的研究提供了一个有价值的参考.

关键词: 一维Frenkel-Kontorova 模型, 同宿轨道, 多周期振荡, 拟周期振荡, 双曲型鞍焦点

Abstract: The dynamic behaviors of homoclinic orbits，multi-period oscillation and quasi-period oscillation of

an atomic chain are investigated by the one-dimensional Frenkel-Kontorova model. Firstly，the hyperbolic saddle

focus existed in the system is decided by the eigenvalues of Jacobian matrix. Secondly，the condition of system generation

homoclinic orbits is determined via Silnikov theorem at the hyperbolic saddle focus. Finally，the numerical

simulation is used to verify the existence of homoclinic orbits，multi-period oscillation and quasi-period oscillation

of the system. The results of this paper also provide a valuable reference for the study of solid friction phenomena.

Key words: one-dimensional Frenkel-Kontorova model, homoclinic orbits, multi-period oscillation, quasiperiod oscillation, hyperbolic saddle focus

康举, 黄头生, 孟天祥, 张化永. 一维 Frenkel－Kontorova 模型原子链的同宿轨和拟周期行为研究 [J]. 大学物理, 2018, 37(12): 26-.

KANG Ju, HUANG Tou-sheng, MENG Tian-xiang, ZHANG Hua-yong. Study of homoclinic orbits and quasi-period behavior of atomic chain in the one-dimensional Frenkel-Kontorova model[J]. College Physics, 2018, 37(12): 26-.

一维 Frenkel－Kontorova 模型原子链的同宿轨和拟周期行为研究

Study of homoclinic orbits and quasi-period behavior of atomic chain in the one-dimensional Frenkel-Kontorova model

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