Chaos and coherence in the conservative three-mode decay interaction

In this work we analyze the influence of chaos on the coherence of the mismatched three-wave interaction. Chaos starts to play a decisive role in the problem when adiabatic approximations leading to an integrable model for the system cease to be valid. In regular regimes where the field levels are sufficiently small, there is a characteristic value for the frequency mismatch of the triplet below which coherence and phase locking are dominant. In chaotic regimes, on the other hand, there is no such value and locking behaves in a more complicated way.