Periodic solutions, global attractivity and oscillation of an impulsive delay host-macroparasite model. (English) Zbl 1165.34350

Summary: We consider the nonlinear impulsive delay host-macroparasite model with periodic coefficients. By means of the continuation theorem of coincidence degree, we establish a sufficient condition for the existence of a positive periodic solution \(\bar{M}(t)\) with strictly positive components. Moreover, we establish a sufficient condition for the global attractivity of \(\bar{M}(t)\) and some sufficient conditions for oscillation of all positive solutions about the positive periodic solution \(\bar{M}(t)\).


34C25 Periodic solutions to ordinary differential equations
34A37 Ordinary differential equations with impulses
34D45 Attractors of solutions to ordinary differential equations
92D25 Population dynamics (general)
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