Stability analysis of a tritrophic model with stage structure in the prey population

Volume 12, Issue 12, pp 765--790 http://dx.doi.org/10.22436/jnsa.012.12.01

Publication Date: July 06, 2019 Submission Date: April 05, 2019 Revision Date: May 31, 2019 Accteptance Date: June 08, 2019

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Authors

Gamaliel Blé - División Académica de Ciencias Básicas, UJAT, Km 1, Carretera Cunduacán-Jalpa de Méndez, Cunduacán, Tabasco, c.p. 86690, México. Miguel Angel Dela-Rosa - División Académica de Ciencias Básicas, CONACyT-UJAT, Km 1, Carretera Cunduacán-Jalpa de Méndez, Cunduacán, Tabasco, c.p. 86690, México. Iván Loreto-Hernández - División Académica de Ciencias Básicas, CONACyT-UJAT, Km 1, Carretera Cunduacán-Jalpa de Méndez, Cunduacán, Tabasco, c.p. 86690, México.

Abstract

We analyze the role of the age structure of a prey in the dynamics of a tritrophic model. We study the effect of predation on a non-reproductive prey class, when the reproductive class of the prey has a defense mechanism. We consider two cases accordingly to the interaction between predator and reproductive class of the prey. In the first case, the functional response is Holling type II and it is possible to show up to two positive equilibria. When we consider a defense mechanism the functional response is Holling type IV. In both cases, we show sufficient parameter conditions to have a stable limit cycle obtained by a supercritical Hopf bifurcation. Some numerical simulations are carried out.

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Keywords

• Hopf's Bifurcation
• tritrophic model
• coexistence of species
• prey age structure

MSC

•  37G15
•  34C23
•  92D40
•  92D25

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