Attraction to Equilibria in Stage-Structured Predator Prey Models and Bio-Control Problems

Controlling invasive species has become an important ecological issue over the last decades. A popular management strategy consists of releasing natural enemies, generally predators. From a mathematical point of view, the study of any realistic problem in bio-control normally involves models remarka...

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Bibliographic Details
Published inJournal of dynamics and differential equations Vol. 31; no. 1; pp. 435 - 450
Main Author Ruiz-Herrera, Alfonso
Format Journal Article
LanguageEnglish
Published New York Springer US 15.03.2019
Springer Nature B.V
Subjects
Applications of Mathematics
Insects
Iterative methods
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
Predator-prey simulation
Iterative method
Transcritical bifurcation
Invasive plants
Global attraction
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Summary:Controlling invasive species has become an important ecological issue over the last decades. A popular management strategy consists of releasing natural enemies, generally predators. From a mathematical point of view, the study of any realistic problem in bio-control normally involves models remarkably resistant to the analysis. In this paper, we propose a new iterative method for studying the dynamical behaviour of a predator-prey model in which an invasive plant is subject to predation of an insect population. We show that the dynamics of the model depends on a suitable scalar function that determines the existence of equilibria.
ISSN:1040-7294
1572-9222
DOI:10.1007/s10884-018-9673-z