Abstract:
ABSTRACT: We consider the synchronization and cessation of oscillation of a positive even
number of planar oscillators that are coupled to their nearest neighbours 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 strength there are both
symmetric and antisymmetric synchronization that corresponds to symmetric and antisymmetric
non-constant periodic solutions respectively. Symmetric synchronization persists for all coupling
strengths while the antisymmetric case exists for only weak coupling strength and disappears to the
origin after a certain coupling strength.
