Analysis of stability and Hopf bifurcation in a fractional Gauss-type predator–prey model with Allee effect and Holling type-III functional response

© 2018, The Author(s). The Kolmogorov model has been applied to many biological and environmental problems. We are particularly interested in one of its variants, that is, a Gauss-type predator–prey model that includes the Allee effect and Holling type-III functional response. Instead of using class...

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Main Authors: Kanokrat Baisad, Sompop Moonchai
Format: Journal
Published: 2018
Online Access:https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85042932995&origin=inward
http://cmuir.cmu.ac.th/jspui/handle/6653943832/48358
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spelling th-cmuir.6653943832-483582018-04-25T10:11:27Z Analysis of stability and Hopf bifurcation in a fractional Gauss-type predator–prey model with Allee effect and Holling type-III functional response Kanokrat Baisad Sompop Moonchai © 2018, The Author(s). The Kolmogorov model has been applied to many biological and environmental problems. We are particularly interested in one of its variants, that is, a Gauss-type predator–prey model that includes the Allee effect and Holling type-III functional response. Instead of using classic first order differential equations to formulate the model, fractional order differential equations are utilized. The existence and uniqueness of a nonnegative solution as well as the conditions for the existence of equilibrium points are provided. We then investigate the local stability of the three types of equilibrium points by using the linearization method. The conditions for the existence of a Hopf bifurcation at the positive equilibrium are also presented. To further affirm the theoretical results, numerical simulations for the coexistence equilibrium point are carried out. 2018-04-25T10:11:27Z 2018-04-25T10:11:27Z 2018-12-01 Journal 16871847 16871839 2-s2.0-85042932995 10.1186/s13662-018-1535-9 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85042932995&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/48358
institution Chiang Mai University
building Chiang Mai University Library
country Thailand
collection CMU Intellectual Repository
description © 2018, The Author(s). The Kolmogorov model has been applied to many biological and environmental problems. We are particularly interested in one of its variants, that is, a Gauss-type predator–prey model that includes the Allee effect and Holling type-III functional response. Instead of using classic first order differential equations to formulate the model, fractional order differential equations are utilized. The existence and uniqueness of a nonnegative solution as well as the conditions for the existence of equilibrium points are provided. We then investigate the local stability of the three types of equilibrium points by using the linearization method. The conditions for the existence of a Hopf bifurcation at the positive equilibrium are also presented. To further affirm the theoretical results, numerical simulations for the coexistence equilibrium point are carried out.
format Journal
author Kanokrat Baisad
Sompop Moonchai
spellingShingle Kanokrat Baisad
Sompop Moonchai
Analysis of stability and Hopf bifurcation in a fractional Gauss-type predator–prey model with Allee effect and Holling type-III functional response
author_facet Kanokrat Baisad
Sompop Moonchai
author_sort Kanokrat Baisad
title Analysis of stability and Hopf bifurcation in a fractional Gauss-type predator–prey model with Allee effect and Holling type-III functional response
title_short Analysis of stability and Hopf bifurcation in a fractional Gauss-type predator–prey model with Allee effect and Holling type-III functional response
title_full Analysis of stability and Hopf bifurcation in a fractional Gauss-type predator–prey model with Allee effect and Holling type-III functional response
title_fullStr Analysis of stability and Hopf bifurcation in a fractional Gauss-type predator–prey model with Allee effect and Holling type-III functional response
title_full_unstemmed Analysis of stability and Hopf bifurcation in a fractional Gauss-type predator–prey model with Allee effect and Holling type-III functional response
title_sort analysis of stability and hopf bifurcation in a fractional gauss-type predator–prey model with allee effect and holling type-iii functional response
publishDate 2018
url https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85042932995&origin=inward
http://cmuir.cmu.ac.th/jspui/handle/6653943832/48358
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