Reversibility vs. synchronization in oscillator lattices

We consider the dynamics of a lattice of phase oscillators with a nearest-neighbor coupling. The clustering hierarchy is described for the case of linear distribution of natural frequencies. We demonstrate that for small couplings prior to the appearance of the first cluster the dynamics is quasi-Hamiltonian: the phase volume is conserved in average, and the spectrum of the Lyapunov exponents is symmetric. We explain this unexpected for a dissipative system phenomenon using the concept of reversibility. We show that for a certain coupling a smooth transition from the quasi-Hamiltonian to the dissipative dynamics occurs, which is a novel type of chaos–chaos transition.