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Existence and stability of periodic solution of a Lotka-Volterra predator-prey model with state dependent impulsive effects. (English) Zbl 1162.34007

An impulsive system of Lotka-Volterra-predator-prey type, according to biological and chemical control strategy for pest is constructed

dx dt=x(t)[b 1 -a 11 x(t)-a 12 y(t)]dy dt=y(t)[-b 2 +a 21 x(t)]xh 1 h 2 ,Δx(t)=0Δy(t)=y(t + )-y(t)=αx=h 1 Δx(t)=x(t + )-x(t)=-px(t)Δy(t)=y(t + )-y(t)=-qy(t)x=h 2 (1)

Sufficient conditions for the existence of

– stable semi-trivial solution of (1)

– order-1 periodic solution of (1)

– positive locally orbitally stable solution of (1)

– positive order-1 periodic solution

are founded.

34A37Differential equations with impulses
34C25Periodic solutions of ODE
92D25Population dynamics (general)