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Multiple periodic solutions for a discrete time model of plankton allelopathy. (English) Zbl 1134.39008
Summary: We study a discrete time model of the growth of two species of plankton with competitive and allelopathic effects on each other
\[ \begin{aligned} N_1(k+1)&= N_1(k)\exp\{r_1(k)- a_{11}(k)N_1(k)- a_{12}(k)N_2(k)- b_1(k)N_1(k)N_2(k)\},\\ N_2(k+1)&= N_2(k)\exp\{r_2(k)- a_{21}(k)N_1(k)- a_{22}(k) N_2(k)- b_2(k)N_1(k)N_2(k)\}. \end{aligned} \] A set of sufficient conditions is obtained for the existence of multiple positive periodic solutions for this model. The approach is based on Mawhin’s continuation theorem of coincidence degree theory as well as some a priori estimates. Some new results are obtained.

MSC:
39A11 Stability of difference equations (MSC2000)
39A12 Discrete version of topics in analysis
92D25 Population dynamics (general)
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References:
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