Dynamical analysis of a new fractional-order predator–prey system with Holling type-III functional

Dynamical analysis of a new fractional-order predator–prey system with Holling type-III functional

Abstract In this paper, we consider a new fractional-order predator–prey model with Holling type-III functional response and stage structure. Based on the Lyapunov stability theory and by constructing a suitable Lyapunov functional, we obtain some sufficient conditions for the existence and uniquene...

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Main Authors: Lihua Dai, Junjie Wang, Yonggen Ni, Bin Xu
Format: Article
Language:English
Published: SpringerOpen 2021-01-01
Series:Advances in Difference Equations
Subjects:
Fractional-order
Predator–prey model
Asymptotic stability
Lyapunov functional
Online Access:https://doi.org/10.1186/s13662-020-03169-9
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spelling doaj-924788f76fe5492ba8cde92cf59dc44a2021-01-31T16:33:21ZengSpringerOpenAdvances in Difference Equations1687-18472021-01-012021111310.1186/s13662-020-03169-9Dynamical analysis of a new fractional-order predator–prey system with Holling type-III functionalLihua Dai0Junjie Wang1Yonggen Ni2Bin Xu3School of Mathematics and Statistics, Southwest UniversityDepartment of Mathematics and Statistics, Puer UniversityDepartment of Mathematics and Statistics, Puer UniversityDepartment of Mathematics and Statistics, Puer UniversityAbstract In this paper, we consider a new fractional-order predator–prey model with Holling type-III functional response and stage structure. Based on the Lyapunov stability theory and by constructing a suitable Lyapunov functional, we obtain some sufficient conditions for the existence and uniqueness of positive solutions and the asymptotic stability of the positive equilibrium to the system. Finally, we give some numerical examples to illustrate the feasibility of our results.https://doi.org/10.1186/s13662-020-03169-9Fractional-orderPredator–prey modelAsymptotic stabilityLyapunov functional
collection DOAJ
language English
format Article
sources DOAJ
author Lihua Dai
Junjie Wang
Yonggen Ni
Bin Xu
spellingShingle Lihua Dai
Junjie Wang
Yonggen Ni
Bin Xu
Dynamical analysis of a new fractional-order predator–prey system with Holling type-III functional
Advances in Difference Equations
Fractional-order
Predator–prey model
Asymptotic stability
Lyapunov functional
author_facet Lihua Dai
Junjie Wang
Yonggen Ni
Bin Xu
author_sort Lihua Dai
title Dynamical analysis of a new fractional-order predator–prey system with Holling type-III functional
title_short Dynamical analysis of a new fractional-order predator–prey system with Holling type-III functional
title_full Dynamical analysis of a new fractional-order predator–prey system with Holling type-III functional
title_fullStr Dynamical analysis of a new fractional-order predator–prey system with Holling type-III functional
title_full_unstemmed Dynamical analysis of a new fractional-order predator–prey system with Holling type-III functional
title_sort dynamical analysis of a new fractional-order predator–prey system with holling type-iii functional
publisher SpringerOpen
series Advances in Difference Equations
issn 1687-1847
publishDate 2021-01-01
description Abstract In this paper, we consider a new fractional-order predator–prey model with Holling type-III functional response and stage structure. Based on the Lyapunov stability theory and by constructing a suitable Lyapunov functional, we obtain some sufficient conditions for the existence and uniqueness of positive solutions and the asymptotic stability of the positive equilibrium to the system. Finally, we give some numerical examples to illustrate the feasibility of our results.
topic Fractional-order
Predator–prey model
Asymptotic stability
Lyapunov functional
url https://doi.org/10.1186/s13662-020-03169-9
work_keys_str_mv AT lihuadai dynamicalanalysisofanewfractionalorderpredatorpreysystemwithhollingtypeiiifunctional
AT junjiewang dynamicalanalysisofanewfractionalorderpredatorpreysystemwithhollingtypeiiifunctional
AT yonggenni dynamicalanalysisofanewfractionalorderpredatorpreysystemwithhollingtypeiiifunctional
AT binxu dynamicalanalysisofanewfractionalorderpredatorpreysystemwithhollingtypeiiifunctional
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