We consider the Schmidt decomposition of a bipartite density operator induced by the Hilbert-Schmidt scalar product, and we study the relation between the Schmidt coefficients and entanglement. First, we define the Schmidt equivalence classes of bipartite states. Each class consists of all the density operators (in a given bipartite Hilbert space) sharing the same set of Schmidt coefficients. N...

In the paper we propose a new synchronization principle. To guarantee synchronization between coupled chaotic oscillators, proper coupling constants are selected by the Liapunov stability theory and Hurwitz Theorem. As an example and application, we prove the conjecture [Wu & Chua, 1994] that synchronization between two chaotic Chua’s circuits can be achieved by using the second state as feedba...

The scaling hypothesis for the coupled chaotic map lattices (CML) is formulated. Scaling properties of the CML in the regime of extensive chaos observed numerically before is justified analytically. The asymptotic Liapunov exponents spectrum for coupled piece-wise linear chaotic maps is found.

Ab~lraet--Methods for design of residence probability (RP) controllers for linear stochastic systems are developed. The design of RP controllers requires the selection of a controller gain and an initial 'lock in' set. The controller gain is obtained by solving a Riccati equation and the initial set is obtained by solving a Liapunov equation. Examples illustrating the suggested design procedure...

We study the existence of continuous periodic solutions of a neutral delay integral equation of advanced type. In the analysis we employ three fixed point theorems: Banach, Krasnosel’skii, and Krasnosel’skii-Schaefer. Krasnosel’skii-Schaefer fixed point theorem requires an a priori bound on all solutions. We employ a Liapunov type method to obtain such bound.