Journal of Applied Mathematics and Stochastic Analysis
Volume 13 (2000), Issue 1, Pages 85-92

Stability investigation of quadratic systems with delay

Vladimir Davydov and Denis Khusainov

Kiev University, Department of Complex Systems Modelling, 64 Vladimirskaya Sreet, Kiev 252033, Ukraine

Received 1 January 1997; Revised 1 March 1999

Copyright © 2000 Vladimir Davydov and Denis Khusainov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Systems of differential equations with quadratic right-hand sides with delay are considered in the paper. Compact matrix notation form is proposed for the systems of such type. Stability investigations are performed by Lyapunov's second method with functions of quadratic form. Stability conditions of quadratic systems with delay, uniformly by argument deviation, and with delay depending on the system's parameters are derived. A guaranteed radius of the ball of asymptotic stability region for zero solution is obtained.