Methods for detecting phase transitions in complex dynamic systems

The paper proposes two methods for detecting transitions between laminar and turbulent behavior using the example of unidirectionally coupled Ressler systems in the band chaos regime. Both methods are based on calculating the probability of diagnosing the turbulent phase and introducing Poincar sections. Depending on the choice of method, you can either reduce the time it takes to find phase transitions or increase the accuracy of determining the moment of transition between two modes.