Periodic solutions of a discrete time stage-structure model (Q864200)

Using a continuation theorem of coincidence degree theory, the authors consider the existence of positive periodic solutions for the discrete periodic stage-structure model with diffusion \[ \begin{aligned} I_{1}(k+1) &= I_{k}\exp \left\{-b(k) - c(k) + a(k)\frac{M_{1}(k)}{I_{1}(k)} \right\}\cr M_{1}(k+1) &= M_{1}(k)\exp \left\{-D_{12}(k) - \alpha(k)M_{1}(k) + \frac{D_{12}(k)M_{2}(k) + c(k)I_{1}(k)}{M_{1}(k)}\right\}\cr M_{2}(k+1) &= M_{2}(k) \exp \left\{-D_{21}(k) - \beta(k) + D_{21}(k)\frac{M_{1}(k)} {M_{2}(k)}\right\},\end{aligned} \] where \(a(k), b(k), c(k), \alpha(k), D_{12}(k), \beta(k)\) and \(D_{21}(k)\) are positive \(\omega\)-periodic sequences and \(\omega\) is a positive integer. The result depends upon the obtainment of a priori bounds for the possible periodic solutions.