Dynamics for a non-autonomous predator-prey system with generalist predator

Dingyong Bai, Jianshe Yu, Meng Fan, Yun Kang

Research output: Contribution to journalArticle

Abstract

In this paper, we study complex dynamics of a non-autonomous predator-prey system with a Holling type II functional response and predator being generalist. We first studied basic dynamics such as boundedness, positive invariance, permanence, non-persistence and globally asymptotic stability. We also provide sufficient conditions for the existence, uniqueness and globally asymptotic stability of positive periodic solutions and boundary periodic solutions of the proposed model when parameters are periodic. We give the integral conditions to prove the extinction of prey and predator and globally asymptotic stability of boundary periodic solutions, and we show that these conditions have more reasonable biological interpretation than those expressed by supremum and infimum of parameters in some literature. We also perform numerical simulations to complement our analytical results and obtain more insights. Some of our numerical simulations indicate that periodic system may promote or suppress the permanence of its autonomous version with parameters being the averages of periodic parameters.

Original languageEnglish (US)
Article number123820
JournalJournal of Mathematical Analysis and Applications
Volume485
Issue number2
DOIs
StatePublished - May 15 2020

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Predator prey systems
Nonautonomous Systems
Predator-prey System
Globally Asymptotic Stability
Predator
Asymptotic stability
Permanence
Periodic Solution
Time varying systems
Computer simulation
Invariance
Numerical Simulation
Integral Condition
Functional Response
Positive Periodic Solution
Periodic Systems
Complex Dynamics
Prey
Supremum
Extinction

Keywords

  • Globally asymptotic stability
  • Non-permanence
  • Periodic solutions
  • Persistence
  • Predator-prey system

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Dynamics for a non-autonomous predator-prey system with generalist predator. / Bai, Dingyong; Yu, Jianshe; Fan, Meng; Kang, Yun.

In: Journal of Mathematical Analysis and Applications, Vol. 485, No. 2, 123820, 15.05.2020.

Research output: Contribution to journalArticle

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