Dynamics of a stochastic delayed Harrison-type predation model: Effects of delay and stochastic components
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 m...
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| Format: | Article |
| Language: | English |
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AIMS Press
2018-11-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2018064 |
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| author | Feng Rao Carlos Castillo-Chavez Yun Kang |
| author_facet | Feng Rao Carlos Castillo-Chavez Yun Kang |
| author_sort | Feng Rao |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-cc68732140694e4db8704276c2922cf1 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2018-11-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-cc68732140694e4db8704276c2922cf12025-01-24T02:41:08ZengAIMS PressMathematical Biosciences and Engineering1551-00182018-11-011561401142310.3934/mbe.2018064Dynamics of a stochastic delayed Harrison-type predation model: Effects of delay and stochastic componentsFeng Rao0Carlos Castillo-Chavez1Yun Kang2School of Physical and Mathematical Sciences, Nanjing Tech University, Nanjing, Jiangsu 211816, ChinaMathematical, Computational and Modeling Sciences Center, Arizona State University, Tempe, AZ 85287-1904, USAMathematical, Computational and Modeling Sciences Center, Arizona State University, Tempe, AZ 85287-1904, USAThis 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.https://www.aimspress.com/article/doi/10.3934/mbe.2018064prey-predator modeltime delayhopf bifurcationstochastic perturbationsstability |
| spellingShingle | Feng Rao Carlos Castillo-Chavez Yun Kang Dynamics of a stochastic delayed Harrison-type predation model: Effects of delay and stochastic components Mathematical Biosciences and Engineering prey-predator model time delay hopf bifurcation stochastic perturbations stability |
| title | Dynamics of a stochastic delayed Harrison-type predation model: Effects of delay and stochastic components |
| title_full | Dynamics of a stochastic delayed Harrison-type predation model: Effects of delay and stochastic components |
| title_fullStr | Dynamics of a stochastic delayed Harrison-type predation model: Effects of delay and stochastic components |
| title_full_unstemmed | Dynamics of a stochastic delayed Harrison-type predation model: Effects of delay and stochastic components |
| title_short | Dynamics of a stochastic delayed Harrison-type predation model: Effects of delay and stochastic components |
| title_sort | dynamics of a stochastic delayed harrison type predation model effects of delay and stochastic components |
| topic | prey-predator model time delay hopf bifurcation stochastic perturbations stability |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2018064 |
| work_keys_str_mv | AT fengrao dynamicsofastochasticdelayedharrisontypepredationmodeleffectsofdelayandstochasticcomponents AT carloscastillochavez dynamicsofastochasticdelayedharrisontypepredationmodeleffectsofdelayandstochasticcomponents AT yunkang dynamicsofastochasticdelayedharrisontypepredationmodeleffectsofdelayandstochasticcomponents |