With the use of multiresolution wavelet analysis, the possibilities of diagnosing changes in the dynamical regimes of complex systems from transient processes depending on the rate of variations of control parameters are studied. Estimates are made of the minimum sample size that allows diagnosing a change in the dynamical regime of systems with self-sustained oscillations on the example of transient processes during the formation or destruction of synchronous chaotic oscillations.

A generalization of the wavelet-transform modulus maxima method to the case of multifractal analysis is proposed, in which the cooperative dynamics of subsystems and the change in the interaction between them are characterized using a joint singularity spectrum. On the example of the phenomenon of chaotic synchronization in the model of interacting Lorentz systems, the possibility of diagnosing a change in the functioning regime in terms of the wavelet-based multifractal formalism is illustrated.