| Abstract: |
| A semelparous Leslie matrix model is an age-structured population model described by a system of difference equations. In a certain class of semelparous Leslie matrix models, either a positive equilibrium is stable and an invariant set on the boundary of the nonnegative cone is unstable or vice versa generically if the number of age-classes is two or three. However, it was shown, recently, that if the number of age-classes is four, this dynamic dichotomy is failed [1]. In this talk, we review this result and examine an attractive invariant loop that emerges when a positive equilibrium is unstable and the boundary of the nonnegative cone does not have an attractor.
[1] R. Kon (2017), Non-synchronous oscillations in four-dimensional nonlinear semelparous Leslie matrix models, Journal of Difference Equations and Applications, 10 pp.1747--1759. |
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