| n维耦合振子格点系统的同步性 |
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| 引用本文： | 马建华,周盛凡. n维耦合振子格点系统的同步性[J]. 数学学报, 2011, 0(2) |
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| 作者姓名： | 马建华 周盛凡 |
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| 作者单位： | 电子科技大学经济与管理学院;上海师范大学应用数学系; |
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| 基金项目： | 国家自然科学基金资助项目(10771139,11071165); 教育部博士点基金项目(200802700002); 上海市人才发展基金项目(2008049) |
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| 摘 要： | 本文通过在相空间中引入新范数的方法研究了Dirichlet,Neumann,周期三个不同边界条件下带有周期外力的n维二阶耦合振子格点系统的同步性.在Dirichlet边界条件下,如果系统非线性项的一阶偏导数有界,则当耦合系数足够大时,系统是有界耗散的并且任意两个解之间是同步的.在Neumann与周期边界条件下,如果不同子系统的外力之间的差和不同子系统的非线性项之间的差都比较小,并且系统是有界耗散的,则当耦合系数足够大时,系统任意一个解的任意两个分量之间是渐近同步的.这两种情况下,当耦合系数c_1→+∞,c_2→+∞时,系统任意一个解的任意两个分量之间是同步的.
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| 关 键 词： | 同步 有界耗散 非恒等振子 |
Synchronization in n-Dimensional Second Order Lattices of Coupled Oscillators |
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| Jian Hua MA School of Economic , Management,University of Electronic Science , Technology of China,Chengdu ,P.R.China Sheng Fan ZHOU. Synchronization in n-Dimensional Second Order Lattices of Coupled Oscillators[J]. Acta Mathematica Sinica, 2011, 0(2) |
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| Authors: | Jian Hua MA School of Economic Management University of Electronic Science Technology of China Chengdu P.R.China Sheng Fan ZHOU |
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| Affiliation: | Jian Hua MA School of Economic and Management,University of Electronic Science and Technology of China,Chengdu 610054,P.R.China Sheng Fan ZHOU Department of Applied Mathematics,Shanghai Normal University,Shanghai 200234,P.R.China |
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| Abstract: | The synchronization of the n-dimensional second order lattices of coupled oscillators with external periodic forces under Dirichlet,Neumann,Periodic boundary conditions are studied by introducing a new norm in the phase space.For the system with Dirichlet boundary condition,if the first order partial derivatives of the nonlinear term are bounded,and the coupled coefficients are both large enough,the system will be bounded dissipative and the solutions of the system will be synchronized to each For the syste... |
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| Keywords: | synchronization bounded dissipative nonidentical oscillators |
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