A Mathematical Model to describe the herd behaviour considering group defense-Reference-Cited by-同舟云学术

A Mathematical Model to describe the herd behaviour considering group defense

Published:2020-01-01 Issue:1 Volume:5 Page:11-24
ISSN:2444-8656
Container-title:Applied Mathematics and Nonlinear Sciences
language:en
Short-container-title:

Author:

de Assis R. A.,Pazim R.¹,Malavazi M. C.¹,Petry P. P. da C.²,de Assis L. M. E.²,Venturino E.³

Affiliation:

1. Instituto de Ciências Naturais Humanas e Sociais , Universidade Federal de Mato Grosso , Av. Alexandre Ferronato 1200, Setor Industrial, 78557267 Sinop , MT, Brazil .

2. Faculdade de Ciências Exatas e Tecnológicas , Universidade do Estado de Mato Grosso , Av. dos Ingás 3001, 78555000 Sinop , MT, Brazil .

3. Dipartimento di Matematica “Giuseppe Peano” , Università di Torino , via Carlo Alberto 10, 10123 Torino, Italy . Member of the INdAM research group GNCS.

Abstract

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.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Engineering (miscellaneous),Modeling and Simulation,General Computer Science

Link

https://www.sciendo.com/pdf/10.2478/amns.2020.1.00002

Reference20 articles.

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2. Luciana Mafalda Elias de Assis, Eduardo Massad, Raul Abreu de Assis, Rubens Pazim, and Ezio Venturino On Periodic Regimes Triggered by Herd Behaviour in Population Systems International Journal of Applied and Computational Mathematics, 5:99, 2019. https://doi.org/10.1007/s40819-019-0689-9

3. Iulia Martina Bulai, Ezio Venturino, Shape effects on herd behavior in ecological interacting population models, Mathematics and Computers in Simulation, 141 (2017) 40–55 https://doi.org/10.1016/j.matcom.2017.04.009

4. T. Caro. Antipredator Defenses in Birds and Mammals. University of Chicago Press, Chicago, 2005.

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