In this report we examine the effects of synchronization within the framework of two classical problems that often arise in studying the behavior of various ensembles. In the first part of the report we consider a system of diffusively coupled nonidentical dynamical systems. To obtain the conditions for synchronization here, we use an approach based on the connection graph stability method. In particular, we obtain the threshold values of the coupling coefficients, that are sufficient to establish a
d-synchronization. In the second part of the report, the problem of nonlinearly (inertially) coupled systems is considered. The results of mathematical modeling here, explain, particularly, the causes and types of «sympathy» between the Huygens's clocks. A rich variety of both regular and chaotic motions in such systems is demonstrated. The calculations show the significant dependence of transient processes on initial conditions.
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