A Mathematical Model to describe the herd behaviour considering group defense

被引：28

作者：

de Assis, R. A. ^{[1
]}

Pazim, R. ^{[1
]}

Malavazi, M. C. ^{[1
]}

Petry, P. P. da C. ^{[2
]}

de Assis, L. M. E. ^{[2
]}

Venturino, E. ^{[3
,4
]}

机构：

[1] Univ Fed Mato Grosso, Inst Ciancias Nat Humanas & Socials, Av Alexandre Ferronato 1200, BR-78557267 Sinop, MT, Brazil

[2] Univ Estado Mato Grosso, Fac Ciencias Exatas & Tecnol, Av Ingas 3001, BR-78555000 Sinop, MT, Brazil

[3] Univ Torino, Dipartimento Matemat Giuseppe Peano, Via Carlo Alberto 10, I-10123 Turin, Italy

[4] INdAM Res Grp GNCS, Rome, Italy

来源：

APPLIED MATHEMATICS AND NONLINEAR SCIENCES | 2020年 / 5卷 / 01期

关键词：

herd behaviour; group defense; predator-prey; bifurcations;

D O I：

10.2478/AMNS.2020.1.00002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：11 / 24

页数：14

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