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

## TL;DR

This paper investigates the complex dynamics, including chaos, in models of locally coupled conservative and dissipative oscillators, linking Hamiltonian systems to the Topaj-Pikovsky phase oscillator model through numerical simulations.

## Contribution

It introduces a Hamiltonian lattice model with local coupling related to the nonlinear Schrödinger equation and demonstrates its complex dynamics and invariant manifolds, extending the Topaj-Pikovsky framework.

## Key findings

- Hamiltonian model exhibits complex, chaotic dynamics.
- Invariant manifolds are exactly equivalent to the Topaj-Pikovsky model.
- Two dissipative models close to the Topaj-Pikovsky system are proposed.

## Abstract

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.