We discuss the dynamics of integrable and non-integrable chains of coupled oscillators under continuous weak position measurements in the semiclassical limit. In this limit, the dynamics are described by the standard stochastic Langevin equation, and we show that the measurement-induced transitions appear as noise- and dissipation-induced chaotic to non-chaotic transitions resembling stochastic synchronization . In non-integrable chains of anharmonically coupled oscillators, the temporal growth of the classical extratime correlator and the broadening of the ballistic light cone, characterized by the Lyapunov exponent and the butterfly velocity, can be observed above the noise or Indicates to stop below. Strength of interaction. Both the Lyapunov exponent and butterfly velocity behave like order parameters and vanish in non-chaotic phases. In addition, butterfly velocities exhibit significant finite-size scaling. For the integrable model, we consider the classical Toda chain and show that the Lyapunov exponent varies non-monotonically with noise intensity, vanishes above the zero noise limit and critical noise, and peaks at intermediate noise intensities. increase. The butterfly velocity of the Toda chain shows a peculiar behavior approaching the integration limit with zero noise intensity.
