Abstract
The existence of phaselocked solutions in chains of weakly coupled oscillators is proven rigorously. The solutions show interesting monotonicity which plays an important role for the existence proofs. Under some conditions, we show that two-dimensional arrays can be decomposed into two one-dimensional problems. With this theory of decomposition, target patterns can be explained. Numerical results are provided to illustrate the theorems on the chain problem and to show traveling waves in the chains and arrays.
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