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Zbl 1022.34070
Stamova, Ivanka M.; Stamov, Gani T.
Lyapunov-Razumikhin method for impulsive functional differential equations and applications to the population dynamics.
(English)
[J] J. Comput. Appl. Math. 130, No.1-2, 163-171 (2001). ISSN 0377-0427

The authors consider the following system of functional-differential equations $$\dot{x}(t)=f(t,x_t),\quad t>t_0,\ t\neq t_k;\qquad x(t_k+0)-x(t_k-0)=I_k(x(t_k-0)),\quad t_k>t_0.$$ They obtain sufficient conditions for stability, uniform stability and asymptotic stability. As an application they investigate an impulsive delay logistic equation. Stability conditions obtained for this equation are not explicit.
[Leonid Berezanski (Beer-Sheva)]
MSC 2000:
*34K20 Stability theory of functional-differential equations
92D25 Population dynamics
34K45 Equations with impulses

Keywords: stability; Lyapunov-Razumikhin function; impulsive functional-differential equations; impulsive delay logistic equation

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