Self-synchronization and controlled synchronization

An attempt is made to give a general formalism for synchronization in dynamical systems encompassing most of the known definitions and applications. The proposed set-up describes synchronization of interconnected systems with respect to a set of functionals and captures peculiarities of both self-synchronization and controlled synchronization. Various illustrative examples are give

Self-synchronization and controlled synchronization of dynamical systems

A general definition of synchronization of dynamical systems is given capturing features of both self-synchronized systems and systems synchronized by means of control. It has been demonstrated for important special cases of "master-slave" and coupled systems that synchronizing control may be designed using feedback linearization or passification methods

A partial synchronization theorem

When synchronization sets in, coupled systems oscillate in a coherent way. It is possible to observealso some intermediate regimes characterized by incomplete synchrony which are referred to aspartial synchronization. The paper focuses on analysis of partial synchronization in networks oflinearly coupled oscillators

Estimation of the region of attraction by first order approximation

Conditions are given that guarantee the convergence of arbitrary solutions of an autonomous dynamical system towards some equilibrium point of the system. The conditions are formulated in terms of matrix inequalities involving a variational equation. A connection with analytic estimates of the Hausdorff dimension of invariant compact sets is give