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Synchronization in lattices of coupled oscillators. (English) Zbl 1194.34056

Summary: We consider coupled nonlinear oscillators with external periodic forces and the Dirichlet boundary conditions. We prove that synchronization occurs provided that the coupling is dissipative and the coupling coefficients are sufficiently large. The synchronization here is of an obvious type - the size of an attractor is comparable to the difference of the subsystems.

MSC:

34C11 Growth and boundedness of solutions to ordinary differential equations
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
34D45 Attractors of solutions to ordinary differential equations
70K20 Stability for nonlinear problems in mechanics
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