一维 Frenkel－Kontorova 模型原子链的同宿轨和拟周期行为研究
收稿日期: 2018-04-16
录用日期: 2018-06-16
网络出版日期: 2019-01-17
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
Received date: 2018-04-16
Accepted date: 2018-06-16
Online published: 2019-01-17
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
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 . DOI: 10.16854 /j.cnki.1000-0712.180230
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.
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