Nonexistence of synchronous orbits and class coexistence in matrix population models. (English) Zbl 1096.39009
Author’s abstract: Existence of synchronous orbits in a general class of matrix population models is considered. Our results show that a matrix population model does not possess a synchronous orbit if the associated directed graph is primitive. Furthermore, it is also shown that if there are no synchronous orbits, then all classes coexist. To illustrate these results, the density dependent Leslie matrix model is analyzed.
Reviewer: Fozi Dannan (Damascus)
MSC:
39A11 | Stability of difference equations (MSC2000) |
92D25 | Population dynamics (general) |
39A12 | Discrete version of topics in analysis |