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Periodic solutions of a discrete two-species competitive model with stage structure. (English) Zbl 1145.34334

Summary: We investigate the following discrete periodic stage-structure model. \(x_1(k+1)=x_1(k)\exp(-a_1(k)+b_1(k)\frac{x_2(k)}{x_1(k)})\), \(x_2(k+1)=x_2(k)\exp(a_2(k)\frac{x_1(k)}{x_2(k)}-b_2(k)-c(k)x_2(k)-\beta_1(k)x_3(k))\), \(x_3(k+1)=x_3(k)\exp(d(k)-\exp(k)x_3(k)-\beta_2(k)x_2(k))\). The sufficient and realistic conditions are obtained for the existence of a positive periodic solution of this system.

MSC:

34C25 Periodic solutions to ordinary differential equations
92D25 Population dynamics (general)
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References:

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