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2019
12
12
ISSN 2008-1898
0
Stability analysis of a tritrophic model with stage structure in the prey population
Stability analysis of a tritrophic model with stage structure in the prey population
en
en
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.
765
790
Gamaliel
Blé
División Académica de Ciencias Básicas
México
gble@ujat.mx
Miguel Angel
Dela-Rosa
División Académica de Ciencias Básicas
México
madelarosaca@conacyt.mx
Iván
Loreto-Hernández
División Académica de Ciencias Básicas
México
iloretohe@conacyt.mx
Hopf's Bifurcation
tritrophic model
coexistence of species
prey age structure
Article.1.pdf
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]
Langevin equation involving one fractional order with three-point boundary conditions
Langevin equation involving one fractional order with three-point boundary conditions
en
en
In this paper, we investigate a class of nonlinear Langevin equation involving one fractional order \(\alpha\in(0, 1]\) with three-point boundary conditions. By the Banach contraction principle and Krasnoselskii's fixed point theorem, the existence and uniqueness results of solutions are obtained. Two examples are given to show the applicability of our main results.
791
798
Ahmed
Salem
Department of Mathematics, Faculty of Science
King Abdulaziz University
Saudi Arabia
ahmedsalem74@hotmail.com
Faris
Alzahrani
Department of Mathematics, Faculty of Science
King Abdulaziz University
Saudi Arabia
Lamya
Almaghamsi
Department of Mathematics, Faculty of Science
Department of Mathematics
King Abdulaziz University
University of Jeddah
Saudi Arabia
Saudi Arabia
Fractional Langevin equations
fixed point theorem
existence and uniqueness
Article.2.pdf
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]