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Existence of positive periodic solution of periodic time-dependent predator-prey system with impulsive effects. (English) Zbl 1058.34051
The following impulsive problem is considered $$\align \dot{N}_1& =N_1(b_1-c_{11}N_1-c_{12}N_2), \\ \dot{N}_2& =N_2(-b_2+c_{21}N_1-c_{22}N_2), \\ \Delta N_1& =c_kN_1,\quad \Delta N_2=d_kN_2,\quad t=\tau_k, \endalign$$ where $b_i(t), c_{ij}(t)$ are continuous, $T$-periodic positive functions, $$c_{k+q}=c_k,~d_{k+q}=d_k,~\tau_{k+q}=\tau_k+T, 1+c_k>0,~1+d_k>0. $$ Under some additional assumptions, using bifurcation theory, the authors prove the existence of a positive periodic solution for this system and discuss some biological applications.

34C25Periodic solutions of ODE
34A37Differential equations with impulses
92D25Population dynamics (general)
34C23Bifurcation (ODE)
Full Text: DOI
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