Interactions Obtained from Basic Mechanistic Principles: Prey Herds and Predators
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...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-10-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/20/2555 |
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| author | Cecilia Berardo Iulia Martina Bulai Ezio Venturino |
| author_facet | Cecilia Berardo Iulia Martina Bulai Ezio Venturino |
| author_sort | Cecilia Berardo |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T06:24:57Z |
| format | Article |
| id | doaj.art-69b0b2fd9cd14f69877b2623fbb6f8a2 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T06:24:57Z |
| publishDate | 2021-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-69b0b2fd9cd14f69877b2623fbb6f8a22023-11-22T19:01:38ZengMDPI AGMathematics2227-73902021-10-01920255510.3390/math9202555Interactions Obtained from Basic Mechanistic Principles: Prey Herds and PredatorsCecilia Berardo0Iulia Martina Bulai1Ezio Venturino2Department of Mathematics and Statistics, University of Helsinki, FI-00014 Helsinki, FinlandDepartment of Mathematics, Informatics and Economics, University of Basilicata, I-85100 Potenza, ItalyGNCS Research Group, INdAM, I-00185 Rome, ItalyWe 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.https://www.mdpi.com/2227-7390/9/20/2555predator–prey modelherd behaviourherd shapelinear functional responseHolling type II functional responsebifurcation analysis |
| spellingShingle | Cecilia Berardo Iulia Martina Bulai Ezio Venturino Interactions Obtained from Basic Mechanistic Principles: Prey Herds and Predators Mathematics predator–prey model herd behaviour herd shape linear functional response Holling type II functional response bifurcation analysis |
| title | Interactions Obtained from Basic Mechanistic Principles: Prey Herds and Predators |
| title_full | Interactions Obtained from Basic Mechanistic Principles: Prey Herds and Predators |
| title_fullStr | Interactions Obtained from Basic Mechanistic Principles: Prey Herds and Predators |
| title_full_unstemmed | Interactions Obtained from Basic Mechanistic Principles: Prey Herds and Predators |
| title_short | Interactions Obtained from Basic Mechanistic Principles: Prey Herds and Predators |
| title_sort | interactions obtained from basic mechanistic principles prey herds and predators |
| topic | predator–prey model herd behaviour herd shape linear functional response Holling type II functional response bifurcation analysis |
| url | https://www.mdpi.com/2227-7390/9/20/2555 |
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