<abstract xmlns="http://www.w3.org/1999/xhtml"><p>A model for predator-prey interactions with herd behaviour is proposed. Novelty includes a smooth transition from individual behaviour (low number of prey) to herd behaviour (large number of prey). The model is analysed using standard stability and bifurcations techniques. We prove that the system undergoes a Hopf bifurcation as we vary the parameter that represents the efficiency of predators (dependent on the predation rate, for instance), giving rise to sustained oscillations in the system. The proposed model appears to possess more realistic features than the previous approaches while being also relatively easier to analyse and understand.</p></abstract>

A model for predator-prey interactions with herd behaviour is proposed. Novelty includes a smooth transition from individual behaviour (low number of prey) to herd behaviour (large number of prey). The model is analysed using standard stability and bifurcations techniques. We prove that the system undergoes a Hopf bifurcation as we vary the parameter that represents the efficiency of predators (dependent on the predation rate, for instance), giving rise to sustained oscillations in the system. The proposed model appears to possess more realistic features than the previous approaches while being also relatively easier to analyse and understand.

A Mathematical Model to describe the herd behaviour considering group defense

Instituto de Ciências Naturais Humanas e Sociais

Faculdade de Ciências Exatas e Tecnológicas

Dipartimento di Matematica “Giuseppe Peano”

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution 4.0 International License.

{"article-title":"A Mathematical Model to describe the herd behaviour considering group defense"}

A model for predator-prey interactions with herd behaviour is proposed. Novelty includes a smooth transition from individual behaviour (low number of prey) to...

A Mathematical Model to describe the herd behaviour considering group defense

Published Online: Jan 31, 2020

Page range: 11 - 24

Received: Mar 09, 2019

Accepted: Sep 23, 2019

DOI: https://doi.org/10.2478/amns.2020.1.00002

Keywords
herd behaviour, group defense, predator-prey, bifurcations

© 2020 R. A. de Assis et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

A Mathematical Model to describe the herd behaviour considering group defense

Published Online: Jan 31, 2020

Page range: 11 - 24

Received: Mar 09, 2019

Accepted: Sep 23, 2019

DOI: https://doi.org/10.2478/amns.2020.1.00002

Keywordsherd behaviour, group defense, predator-prey, bifurcations

© 2020 R. A. de Assis et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
herd behaviour, group defense, predator-prey, bifurcations