Global dynamics of a special class of nonlinear semelparous Leslie matrix models

Abstract

This paper considers the dynamics of nonlinear semelparous Leslie matrix models. First, a class of semelparous Leslie matrix models is shown to be dynamically consistent with a certain system of Kolmogorov difference equations with cyclic symmetry. Then, the global dynamics of a special class of the latter is fully determined. Combining together, we obtain a special class of semelparous Leslie matrix models which possesses generically either a globally asymptotically stable positive equilibrium or a globally asymptotically stable cycle. The result shows that the periodic behaviour observed in periodical insects can occur as a globally stable phenomenon.

Mathematical Model of Iteroparous and Semelparous Species Interaction

“…In some studies, species in an ecosystem can be categorized based on their reproductive strategy, including species with semelparous and iteroparous strategy. Research on semelparous species can be seen in [1]- [3]. Then, research on iteroparous species can be seen in [4]- [6].…”

“…These studies can be in the form of single species and multispecies cases. Several studies on single species cases include in [3], [8], [9], and many more. Then, several multispecies studies examine the effect of density-dependent on the Leslie matrix model which is one of the nonlinear models of the Leslie matrix model.…”