Abstract
We consider the synchronization and cessation of oscillation of a positive even number of planar oscillators that are coupled to their nearest neighbors on one, two, and three dimensional integer lattices via a linear and symmetric diffusion-like path. Each oscillator has a unique periodic solution that is attracting. We show that for certain coupling strengths there are both symmetric and antisymmetric synchronization that corresponds to symmetric and antisymmetric nonconstant periodic solutions respectively. Symmetric synchronization persists for all coupling strengths while the antisymmetric case exists for only weak coupling strengths and disappears to the origin after a certain coupling strength. AMS(MOS) subject classifications: 34C24, 34C22, 34C14 Keywords: Lattice differential equations, Bravais lattice, synchronization, oscillator death. (Af. J. of Science and Technology: 2003 4(1): 78-84)
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