Interactions Obtained from Basic Mechanistic Principles: Prey Herds and Predators

Cecilia Berardo, Iulia Martina Bulai and Ezio Venturino
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Cecilia Berardo: Department of Mathematics and Statistics, University of Helsinki, FI-00014 Helsinki, Finland
Iulia Martina Bulai: Department of Mathematics, Informatics and Economics, University of Basilicata, I-85100 Potenza, Italy
Ezio Venturino: GNCS Research Group, INdAM, I-00185 Rome, Italy

Mathematics, 2021, vol. 9, issue 20, 1-18

Abstract: We investigate four predator–prey Rosenzweig–MacArthur models in which the prey exhibit herd behaviour and only the individuals on the edge of the herd are subjected to the predators’ attacks. The key concept is the herding index, i.e., the parameter defining the characteristic shape of the herd. We derive the population equations from the individual state transitions using the mechanistic approach and time scale separation method. We consider one predator and one prey species, linear and hyperbolic responses and the occurrence of predators’ intraspecific competition. For all models, we study the equilibria and their stability and we give the bifurcation analysis. We use standard numerical methods and the software Xppaut to obtain the one-parameter and two-parameter bifurcation diagrams.

Keywords: predator–prey model; herd behaviour; herd shape; linear functional response; Holling type II functional response; bifurcation analysis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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