Abstract:
We consider a system of differential equations with two delay parameters describing the interaction of predators and prey. Under non-negative initial conditions, we prove the non-negativity and boundedness of solutions. We specify conditions for the coefficients of the system, under which the components of the solution stabilize to zero at infinity. Using Lyapunov–Krasovskii functionals we establish estimates of the stabilization rate.
Keywords:delay differential equations, predator–prey model, estimates for solutions, Lyapunov–Krasovskii functional
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