@article{405c64a825af4e55bd6e9d093c250dce,
title = "Rotation number of the overdamped Frenkel–Kontorova model with ac-driving",
abstract = "The dynamical behavior of the overdamped and overdamped limit cases of the Frenkel–Kontorova model with ac-driving is studied. The relationship is established between the average velocity of the particles and the rotation number of the orientation preserving homeomorphism on the circle induced from the Poincar{\'e} map. The dynamical behavior for both cases is determined completely by the rotation number. Numerical results are also provided for the second order system to support the theoretical conclusions.",
keywords = "Average velocity, Mode-locking, Orientation preserving homeomorphism, Overdamped Frenkel-Kontorova model, Rotation number",
author = "Bambi Hu and Wen-Xin Qin and Zhigang Zheng",
note = "Funding Information: This work is supported in part by grants from the Hong Kong Research Grants Council (RGC)and the Hong Kong Baptist University Faculty Research Grant (FRG), and in part by the Special Funds for Major State Basic Research Projects, National Natural Science Foundation of China and Natural Science Foundation of Jiangsu Province. WXQ is indebted to Prof. Oleg Braun, Dr. Lei Yang and Dr. Jasmina Teksi{\'c} for helpful discussions. ZHENG is also supported by Foundation for the Author of National Excellent Doctoral Dissertation of PR China, the TRAPOYT in Higher Education Institutions of MOE, the Fund for Doctoral Training of MOE, the Huo-Ying-Dong Educational Funds for Excellent Young Teachers, and the Hong Kong Croucher Foundation. Publisher copyright: {\textcopyright} 2005 Elsevier B.V.",
year = "2005",
month = sep,
day = "1",
doi = "10.1016/j.physd.2005.06.022",
language = "English",
volume = "208",
pages = "172--190",
journal = "Physica D: Nonlinear Phenomena",
issn = "0167-2789",
publisher = "Elsevier B.V.",
number = "3-4",
}