Jian Hua MA, Sheng Fan ZHOU
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 other. For the system with Neumann or Periodic boundary condition, if the variation of the out force of different subsystems and the variation of the nonlinear terms of different subsystems are both small, the system is bounded dissipative and the coupled coefficients are both large enough, then all the components of any one solution of the system will be asymptotic synchronized to each other. Moreover, for the above two cases, when the coupled coefficients c1 → +∞, c2 → +∞, all the components of any one solution of the systems will be synchronized to each other.