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On the existence of positive periodic solutions to a Lotka-Volterra cooperative population model with multiple delays. (English) Zbl 1139.34317
Summary: The author studies the existence of positive periodic solutions to a Lotka-Volterra cooperative population model with multiple delays as follows $$\multline x_i'(t)=x_i(t)\left[r_i(t)-p_{ii}(t)x_i(t)+\sum^n_{k\ne i}p_{ik}(t)x_k(t)-\sum^n_{j=1}q_{ij}(t)x_i(t-\tau_{ij}(t))+\right.\\ \left.\sum^n_{k\ne i}\sum^n_{j=1}c_{ikj}(t)x_k(t-\gamma_{ikj}(t))\right],\quad (i=1,2,\dots,n).\endmultline$$ By using Mawhin’s continuation theorem of coincidence degree principle, a new result is obtained.

34K13Periodic solutions of functional differential equations
92D25Population dynamics (general)
34K60Qualitative investigation and simulation of models
Full Text: DOI
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