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Periodic solutions of a periodic Lotka–Volterra system with delays. (English) Zbl 1069.34099
Using the continuation theorem of the coincidence degree theory proposed by Gaines and Mawhin, the authors obtain sufficient conditions for the existence of a positive periodic solution of the following delay model \[ u_i'(t)=u_i(t)\left[b_i(t)-\sum_{k=1}^na_{ik}(t)u_k(t-\tau_{ik}(t))-\sum_{k=1}^mc_{ik}(t)v_k(t-\sigma_{ik}(t))\right],\;i=1,\cdots,n, \]
\[ v_j'(t)=v_j(t)\left[-r_j(t)-\sum_{k=1}^nd_{ik}(t)u_k(t-\delta_{ik}(t))-\sum_{k=1}^me_{ik}(t)v_k(t-\theta_{ik}(t))\right],\;j=1,\cdots,m. . \]
Reviewer: Yuji Liu (Yueyang)

MSC:
34K13 Periodic solutions to functional-differential equations
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