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Global stability in a differential equation with piecewisely constant arguments. (English) Zbl 0993.34052
The author considers a differential equation with piecewise constant arguments of the form \[ N'(t) = r(t)(-\mu N(t) + \sum_{i=0}^{m} P_i\exp{-r_i N([t-i])}), t\geq 0. \] Asymptotic properties of the coefficient \(r(t)\) are used to define sufficient conditions for the global stability of a positive equilibrium.

MSC:
34D23 Global stability of solutions to ordinary differential equations
34K20 Stability theory of functional-differential equations
34A36 Discontinuous ordinary differential equations
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