naa a22 4500 510809642 CHVBK 20180411083436.0 cr unu---uuuuu 180411e20131101xx s 000 0 eng 10.1134/S1064230713040114 doi (NATIONALLICENCE)springer-10.1134/S1064230713040114 Existence and construction of a function with sign semidefinite derivative for dynamic systems [Elektronische Daten] [A. Kovalev, V. Nespirnyi] The problem of finding a function with sign semidefinite derivative along the solutions to the system of ordinary differential equations is considered. It is shown that a sufficient existence condition is the existence of trajectories that leave a neighborhood of the equilibrium point both in forward or backward time. Two approaches to the construction of the desired function in the autonomous and nonautonomous cases are proposed. The results are illustrated by the example of a nonlinear autonomous system (Artstein's circle). Pleiades Publishing, Ltd., 2013 Kovalev A. Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, Donetsk, Ukraine aut Nespirnyi V. Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, Donetsk, Ukraine aut Journal of Computer and Systems Sciences International Springer US; http://www.springer-ny.com 52/6(2013-11-01), 843-853 1064-2307 52:6<843 2013 52 11488 https://doi.org/10.1134/S1064230713040114 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1134/S1064230713040114 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Kovalev A. Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, Donetsk, Ukraine aut NATIONALLICENCE 700 1- Nespirnyi V. Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, Donetsk, Ukraine aut NATIONALLICENCE 773 0- Journal of Computer and Systems Sciences International Springer US; http://www.springer-ny.com 52/6(2013-11-01), 843-853 1064-2307 52:6<843 2013 52 11488 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer