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Lyapunov-Razumikhin method for impulsive functional differential equations and applications to the population dynamics. (English) Zbl 1022.34070

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.

MSC:

34K20 Stability theory of functional-differential equations
92D25 Population dynamics (general)
34K45 Functional-differential equations with impulses
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