А.В. Ласунский.
О сохранении устойчивого положения равновесия при дискретизации системы
// Труды КарНЦ РАН. No 4. Сер. Математическое моделирование и информационные технологии. 2014. C. 87-92
А.V. Lasunsky. Maintaining steady-state equilibrium after discretization of the system // Transactions of Karelian Research Centre of Russian Academy of Science. No 4. Mathematical Modeling and Information Technologies. 2014. Pp. 87-92
Keywords: preservation of stability after discretization, Lyapunov's first method, nonautonomous Lotka-Volterra model
With the help of Lyapunov's first method we obtained sufficient conditions for maintaining the equilibrium state and its asymptotic stability after discretization of a nonautonomous system of second order differential equations. The result is illustrated by a modified Lotka-Volterra model in which part of the prey population is inaccessible for the predator.
