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Stability of solutions in the predator-prey model with delay. (Russian. English summary) Zbl 1399.34261

Summary: We consider a system of delay differential equations describing the interaction between two populations, the predators and the prey. We study the asymptotic stability of stationary solutions to this system. Using the modified Lyapunov-Krasovskiĭ functional we establish estimates for solutions characterizing the rate of convergence to the stationary solutions.

MSC:

34K60 Qualitative investigation and simulation of models involving functional-differential equations
34K20 Stability theory of functional-differential equations
34K25 Asymptotic theory of functional-differential equations
92D25 Population dynamics (general)
34K21 Stationary solutions of functional-differential equations
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