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.