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Existence of positive periodic solutions for a nonautonomous neutral delay n-species competitive model with impulses. (English) Zbl 1211.34104

Sufficient conditions for the existence of positive periodic solutions are obtained for the following system
\[ \begin{split} {N_i}'(t)=N_i(t)\left[r_i(t)-\sum_{j=1}^n a_{ij}(t) N_j(t)-\sum_{j=1}^n b_{ij}(t) \int_{-\infty}^t k_{ij}(t-s)N_j(s)\,ds\right. \\ \left. -\sum_{j=1}^n c_{ij}(t) N_j(t-\tau_{ij}(t))(t)-\sum_{j=1}^n d_{ij}(t){ N_j}'(t-\gamma_{ij}(t))(t)\right], \end{split} \]
\(\Delta N_i(t_k)=\lambda_{ik}N_i(t_k),~ i=1,\dots,n,~ k=1,2\dots . \)

MSC:

34K60 Qualitative investigation and simulation of models involving functional-differential equations
34K40 Neutral functional-differential equations
34K13 Periodic solutions to functional-differential equations
34K45 Functional-differential equations with impulses
92D25 Population dynamics (general)
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References:

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