Dynamics of phases and chaos in models of locally coupled conservative or dissipative oscillators

We discuss Hamiltonian model of oscillator lattice with local coupling. Model describes spatial modes of nonlinear Schr\"{o}dinger equation with periodic tilted potential. The Hamiltonian system manifests reversibility of Topaj - Pikovsky phase oscillator lattice. Furthermore, the Hamiltonian system has invariant manifolds with dynamics exactly equivalent to the Topaj - Pikovsky model. We demonstrate the complexity of dynamics with results of numerical simulations. We also propose two dissipative models close to Topaj - Pikovsky system.