SACTA, Vol.6, No.1, 2004 49 ABOUT SOME FEATURES OF GENERAL METHOD OF LYAPUNOV FUNCTIONALS CONSTRUCTION V. Kolmanovskii 1 and L. Shaikhet 2 1/ Moscow Institute of Electronics and Mathematics, Novospasskii 3-1-20, Moscow 109172, Russia 2/ Department of Higher Mathematics, Donetsk State University of Management, Chelyuskintsev, 163-a, Donetsk 83015, Ukraine e-mail: vkolmano@mtu-net.ru, leonid.shaikhet@usa.net Recommended by: V. B. Bajic Received: 02 April, 2004 Accepted in the final form: 28 April, 2004 Abstract. Many stability results in the theory of stochastic hereditary systems and their applications were obtained by construction of appropriate Lyapunov functionals. One general method of Lyapunov functionals construction was proposed and developed by the authors during last decade for stability investigation of deterministic and stochastic functional-differential and difference equations. In this paper a survey of some typical examples of this method application and at the same time some new features of this method for stochastic functional differential equations of neutral type are shown, which allow to use the method more effectively. The considered method is illustrated by a lot of figures of stability regions obtained by numerical calculations. Keywords: Stochastic systems, delay, stability, Lyapunov functionals construction 1 Statement of the problem A lot of processes in automatic regulation, physics, mechanics, biology, ecology, economy etc. can be modelled by functional differential equations [1-14]. Many stability results in the theory of func- tional differential equations and their applications were obtained using appropriate Lyapunov function- als. One general method of Lyapunov functionals construction both for deterministic and stochastic functional-differential and difference equations was proposed and developed by authors in [15-29]. Some applications of this method for stability investigation of the mathematical models of some real biological and mechanical systems are considered in [30-32]. Here a survey of some typical examples and some new features of this method for stochastic differential equations of neutral type are shown, which allow to use the method more effectively. A lot of figures with stability regions obtained by numerical calculations illustrate the considered method.