Synchronization in lattices of coupled oscillators with Neumann/periodic boundary conditions. (English) Zbl 1067.34052

Summary: We consider a lattice of coupled Duffing oscillators with external periodic forces and Neumann or periodic boundary conditions. We prove that asymptotic synchronization occurs provided the coupling system is dissipative and coefficients of coupling are sufficiently large. We determine dependence of synchronization coefficients on lattice size.


34D05 Asymptotic properties of solutions to ordinary differential equations
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
37L60 Lattice dynamics and infinite-dimensional dissipative dynamical systems
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