Abstract

This paper investigates the complex dynamics of a Harrison-type predator-prey model that incorporating: (1) A constant time delay in the functional response term of the predator growth equation; and (2) environmental noise in both prey and predator equations. We provide the rigorous results of our model including the dynamical behaviors of a positive solution and Hopf bifurcation. We also perform numerical simulations on the effects of delay or/and noise when the corresponding ODE model has an interior solution. Our theoretical and numerical results show that delay can either remain stability or destabilize the model; large noise could destabilize the model; and the combination of delay and noise could intensify the periodic instability of the model. Our results may provide us useful biological insights into population managements for prey-predator interaction models.

Original languageEnglish (US)
Pages (from-to)1401-1423
Number of pages23
JournalMathematical biosciences and engineering : MBE
Volume15
Issue number6
DOIs
StatePublished - Dec 1 2018

Keywords

  • Hopf bifurcation
  • Prey-predator model
  • stability
  • stochastic perturbations
  • time delay

ASJC Scopus subject areas

  • Modeling and Simulation
  • Agricultural and Biological Sciences(all)
  • Computational Mathematics
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Dynamics of a stochastic delayed Harrison-type predation model: Effects of delay and stochastic components'. Together they form a unique fingerprint.

  • Cite this