MONOTONICITY OF PHASELOCKED SOLUTIONS IN CHAINS AND ARRAYS OF NEAREST-NEIGHBOR COUPLED OSCILLATORS

The existence of phaselocked solutions in chains of weakly coupled osc illators is proven rigorously. The solutions show interesting monotoni city which plays an important role for the existence proofs. Under som e conditions, we show that two-dimensional arrays can be decomposed in to two one-dimensional problems. With this theory of decomposition, ta rget patterns can be explained. Numerical results are provided to illu strate the theorems on the chain problem and to show traveling waves i n the chains and arrays.