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Existence of positive periodic solutions of nonlinear discrete model exhibiting the Allee effect. (English) Zbl 1087.39015
Using the coincidence degree theorem as well as some a priori estimates, the authors establish a sufficient condition for the existence of positive periodic solution to the discrete nonlinear delay population model with Allee effect \[ x(n+1)=x(n)\exp(a(n)+b(n)x^p(n-\omega)-c(n)x^q(n-\omega)), \] where \(a(n)\), \(b(n)\), and \(c(n)\) are positive sequences of period \(\omega\) and \(p\) and \(q\) are positive integers.

MSC:
39A11 Stability of difference equations (MSC2000)
92D25 Population dynamics (general)
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