Synchronization and oscillator death in diffusively coupled lattice oscillators

Abstract EN

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 strength there are both symmetric and ant symmetric synchronization that corresponds to symmetric and ant symmetric non-constant periodic solutions respectively.

Symmetric synchronization persists for all coupling strengths while the ant symmetric case exists for only weak coupling strength and disappears to the origin after a certain coupling strength.