Border collision bifurcations in a generalized model of population dynamics
type: Item
instance of: scholarly article
title: Border collision bifurcations in a generalized model of population dynamics
zbMATH Open document ID: 1417.92136
DOI: 10.1155/2016/9724139
author: Lilia M. Ladino
author: Cristiana Mammana
author: Elisabetta Michetti
author: Jose C. Valverde
published in: Discrete Dynamics in Nature and Society
publication date: 2019-02-19T00:00:00Z
review text: Summary: We analyze the dynamics of a generalized discrete time population model of a two-stage species with recruitment and capture. This generalization, which is inspired by other approaches and real data that one can find in literature, consists in considering no restriction for the value of the two key parameters appearing in the model, that is, the natural death rate and the mortality rate due to fishing activity. In the more general case the feasibility of the system has been preserved by posing opportune formulas for the piecewise map defining the model. The resulting two-dimensional nonlinear map is not smooth, though continuous, as its definition changes as any border is crossed in the phase plane. Hence, techniques from the mathematical theory of piecewise smooth dynamical systems must be applied to show that, due to the existence of borders, abrupt changes in the dynamic behavior of population sizes and multistability emerge. The main novelty of the present contribution with respect to the previous ones is that, while using real data, richer dynamics are produced, such as fluctuations and multistability. Such new evidences are of great interest in biology since new strategies to preserve the survival of the species can be suggested.
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 39A60
zbMATH DE Number: 7025687
Wikidata QID: Q59123705
describes a project that uses: DMC
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2016/9724139
OpenAlex ID: W2398546250
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description: scientific article; zbMATH DE number 7025687