A Generalist Predator and the Planar Zero-Hopf Bifurcation

被引：6

作者：

Miguel Valenzuela, Luis ^{[1
]}

Falconi, Manuel ^{[2
]}

Ble, Gamaliel ^{[3
]}

机构：

[1] UJAT, Div Acad Multidisciplinaria Jalpa de Mendez, Carretera Nacajuca Jalpa de Mendez, Jalpa De Mendez 86205, Tabasco, Mexico

[2] Univ Nacl Autonoma Mexico, Fac Ciencias, Dept Matemat, C Univ, Mexico City 04510, DF, Mexico

[3] UJAT, Div Acad Ciencias Basicas, Km 1 Carretera Cunduacan Jalpa, Cunduacan 86690, Tabasco, Mexico

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2017年 / 27卷 / 03期

关键词：

Predator-prey model; Hopf bifurcation; planar zero-Hopf bifurcation; Holling-Tanner model; generalist predator; PREY SYSTEM; STABILITY; MODEL;

D O I：

10.1142/S0218127417500341

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A typical approach for searching periodic orbits of planar dynamical systems is through the Hopf bifurcation. In this work we present a family of predator-prey models with a generalist predator which does not exhibit a Hopf bifurcation, but a planar zero-Hopf bifurcation; that means, in the whole bifurcation process the eigenvalues of the linear approximation around the equilibrium points remain as pure imaginary. Similar models with a nongeneralist predator always possess a Hopf bifurcation.

引用

页数：12

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