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

Fingerprint

Noise
predation
Predator
predators
Model
Prey-predator
Functional Response
Predator-prey Model
Complex Dynamics
Prey
Hopf bifurcation
Dynamical Behavior
predator-prey relationships
Hopf Bifurcation
Positive Solution
Time Delay
Interior
Growth
Time delay
Population

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

Cite this

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title = "Dynamics of a stochastic delayed Harrison-type predation model: Effects of delay and stochastic components",
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.",
keywords = "Hopf bifurcation, Prey-predator model, stability, stochastic perturbations, time delay",
author = "Feng Rao and Carlos Castillo-Chavez and Yun Kang",
year = "2018",
month = "12",
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doi = "10.3934/mbe.2018064",
language = "English (US)",
volume = "15",
pages = "1401--1423",
journal = "Mathematical Biosciences and Engineering",
issn = "1547-1063",
publisher = "Arizona State University",
number = "6",

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TY - JOUR

T1 - Dynamics of a stochastic delayed Harrison-type predation model

T2 - Effects of delay and stochastic components

AU - Rao, Feng

AU - Castillo-Chavez, Carlos

AU - Kang, Yun

PY - 2018/12/1

Y1 - 2018/12/1

N2 - 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.

AB - 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.

KW - Hopf bifurcation

KW - Prey-predator model

KW - stability

KW - stochastic perturbations

KW - time delay

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