Applied Mathematics and Mechanics (English Edition) ›› 2003, Vol. 24 ›› Issue (5): 521-526.
郑永爱1,2, 刘曾荣2
Email Alert
RSS收稿日期:2001-10-26
修回日期:2002-09-20
出版日期:2003-05-18
发布日期:2003-05-18
基金资助:ZHENG Yong-ai1,2, LIU Zeng-rong2
Received:2001-10-26
Revised:2002-09-20
Online:2003-05-18
Published:2003-05-18
Supported by:摘要： It is proven that the existence of nonlinear solutions with time period in one-dimensional coupled map lattice with nearest neighbor coupling. This is a class of systems whose behavior can be regarded as infinite array of coupled oscillators. A method for estimating the critical coupling strength below which these solutions with time period persist is given. For some particular nonlinear solutions with time period,exponential decay in space is proved.
中图分类号:
郑永爱;刘曾荣. PERIODIC SOLUTIONS IN ONE-DIMENSIONAL COUPLED MAP LATTICES[J]. Applied Mathematics and Mechanics (English Edition), 2003, 24(5): 521-526.
ZHENG Yong-ai;LIU Zeng-rong. PERIODIC SOLUTIONS IN ONE-DIMENSIONAL COUPLED MAP LATTICES[J]. Applied Mathematics and Mechanics (English Edition), 2003, 24(5): 521-526.
| [1] Crutcbfield J P, Kaneko K. Phenomenology of spatio-temporal chaos directions in chaos[J].World Scientific Series on Directions in Condensed Matter Physics, 1987,1(3):272-353. [2] Kaneko K. Pattem dynamics in spatiotemporal chaos[J]. Physica D,1989,34(1):1-41. [3] Coutinho R, Fernandez B. Extended symbolic dynamic in bi stable CML: Existence and stability of fronts[J]. Physica D, 1997,108(1):60-80. [4] Abel M, Spicci M. Nonlinear localized periodic solutions in a coupled map lattice[J]. Physica D,1998,119(1):22-33. [5] Aubry S, Abramovici G. Chaotic trajectories in the standard map, the concept of anti-integrability[J]. Physica D, 1990,43(2): 199-219. [6] Mackay R S, Aubry S. Proof of existence of breathers for time-reversible or Hamiltonian networks of weakly coupled oscillators[J]. Nonlinearity, 1994,7(6): 1623-1643. [7] Aubry S. Breathers in nonlinear lattices:existence, linear stability and quantization[J]. Physica D,1997,103(3):201-250. [8] Zeidler E. Nonlinear Functional Analysis and Its Applications, Fixed-Pointed Theorem[M].New York, Berlin, Heidelberg, Tokyo: Springer-Verlag, 1986. [9] Baesens C, Mackay R S. Exponential localisation of linear response in networks with exponentially decaying coupling[J]. Nonlinearity, 1997,10(4):931-940. |
| [1] | Shujun YOU, Boling GUO. Global solution for quantum Zakharov equations[J]. Applied Mathematics and Mechanics (English Edition), 2017, 38(4): 603-616. |
| [2] | Shan JIANG, Longxiang DAI, Hao CHEN, Hongping HU, Wei JIANG, Xuedong CHEN. Folding beam-type piezoelectric phononic crystal with low-frequency and broad band gap[J]. Applied Mathematics and Mechanics (English Edition), 2017, 38(3): 411-422. |
| [3] | Lihua LIU, Chaolu TEMUER. Symmetry analysis of modified 2D Burgers vortex equation for unsteady case[J]. Applied Mathematics and Mechanics (English Edition), 2017, 38(3): 453-468. |
| [4] | W. PAULSEN, M. MANNING. Finding vibrations of inclined cable structures by approximately solving governing equations for exterior matrix[J]. Applied Mathematics and Mechanics (English Edition), 2015, 36(11): 1383-1402. |
| [5] | A. K. VASHISHTH, A. DAHIYA, V. GUPTA. Generalized Bleustein-Gulyaev type waves in layered porous piezoceramic structure[J]. Applied Mathematics and Mechanics (English Edition), 2015, 36(9): 1223-1242. |
| [6] | A. M. SIDDIQUI, H. ASHRAF, A. WALAIT, T. HAROON. On study of horizontal thin film flow of Sisko fluid due to surface tension gradient[J]. Applied Mathematics and Mechanics (English Edition), 2015, 36(7): 847-862. |
| [7] | Zhijie SHI, Yuesheng WANG, Chuanzeng ZHANG. Band structure calculations of in-plane waves in two-dimensional phononic crystals based on generalized multipole technique[J]. Applied Mathematics and Mechanics (English Edition), 2015, 36(5): 557-580. |
| [8] | Wancheng SHENG;Ying ZENG. Generalized δ-entropy condition to Riemann solution for Chaplygin gas in traffic flow[J]. Applied Mathematics and Mechanics (English Edition), 2015, 36(3): 353-364. |
| [9] | Yinshan YUN;Chaolu TEMUER. Classical and nonclassical symmetry classifications of nonlinear wave equation with dissipation[J]. Applied Mathematics and Mechanics (English Edition), 2015, 36(3): 365-378. |
| [10] | Chao MIN;Nanjing HUANG;Zhibin LIU;Liehui ZHANG. Existence of solutions for implicit fuzzy differential inclusions[J]. Applied Mathematics and Mechanics (English Edition), 2015, 36(3): 401-416. |
| [11] | 陈学慧;郑连存;张欣欣. MHD flow of power-law fluid on moving surface with power-law velocity and special injection/blowing[J]. Applied Mathematics and Mechanics (English Edition), 2014, 35(12): 1555-1564. |
| [12] | 杨曼丽;卢志明;刘宇陆. Self-similar behavior for multicomponent coagulation[J]. Applied Mathematics and Mechanics (English Edition), 2014, 35(11): 1353-1360. |
| [13] | 高军;罗纪生. Mode decomposition of nonlinear eigenvalue problems and application in flow stability[J]. Applied Mathematics and Mechanics (English Edition), 2014, 35(6): 667-674. |
| [14] | H. YASMIN;T. HAYAT;A. ALSAEDI;H. H. ALSULAMI. Peristaltic flow of Johnson-Segalman fluid in asymmetric channel with convective boundary condition[J]. Applied Mathematics and Mechanics (English Edition), 2014, 35(6): 697-716. |
| [15] | 张燕 林平 司新辉. Perturbation solutions for asymmetric laminar flow in porous channel with expanding and contracting walls[J]. Applied Mathematics and Mechanics (English Edition), 2014, 35(2): 203-220. |
| 阅读次数 | ||||||
|
全文 |
|
|||||
|
摘要 |
|
|||||
