Dynamical analysis of a fractional-order predator-prey model incorporating a prey refuge

In this paper, a fractional-order predator-prey model incorporating a prey refuge is proposed. We first prove the existence, uniqueness, non-negativity and boundedness of the solutions for the considered model. Moreover, we also analyze the existence of various equilibrium points, and some sufficien...

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Bibliographic Details
Published inJournal of applied mathematics & computing Vol. 54; no. 1-2; pp. 435 - 449
Main Authors Li, Hong-Li, Zhang, Long, Hu, Cheng, Jiang, Yao-Lin, Teng, Zhidong
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2017
Springer Nature B.V
Subjects
Applied mathematics
Asymptotic methods
Computational Mathematics and Numerical Analysis
Computer simulation
Equilibrium
Extinction
Mathematical analysis
Mathematical and Computational Engineering
Mathematical models
Mathematics
Mathematics and Statistics
Mathematics of Computing
Original Research
Predator-prey simulation
Simulation
Theory of Computation
Uniqueness
Prey refuge
34D23
92D25
Global asymptotic stability
Fractional-order
Predator-prey model
34A08
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Summary:In this paper, a fractional-order predator-prey model incorporating a prey refuge is proposed. We first prove the existence, uniqueness, non-negativity and boundedness of the solutions for the considered model. Moreover, we also analyze the existence of various equilibrium points, and some sufficient conditions are derived to ensure the global asymptotic stability of the predator-extinction equilibrium point and coexistence equilibrium point. Finally, some numerical simulations are carried out for illustrating the analytic results.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1598-5865
1865-2085
DOI:10.1007/s12190-016-1017-8