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On the dynamics of a discrete pest-natural enemy model with Holling II response and stochastic perturbations.

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Title: On the dynamics of a discrete pest-natural enemy model with Holling II response and stochastic perturbations.
Authors: Liu, Bing1 (AUTHOR) bingliu@mail.asnc.edu.cn, Zhu, Shimei1,2 (AUTHOR), Wen, Buyu3 (AUTHOR), Qi, Haokun1 (AUTHOR)
Source: Mathematics & Computers in Simulation. Aug2026, Vol. 246, p477-490. 14p.
Subjects: White noise, Stochastic difference equations, Statistical models, White noise theory, Biological extinction, Population dynamics, Mathematical models, Computer simulation
Abstract: The survival environment of pests and natural enemies is often subject to various stochastic factors, and the introduction of white noise can better simulate such uncertainty. Compared to continuous models, discrete models are more accurate in describing the situations where the successive generations of many species in nature are non-overlapping and the data of biological samples are usually collected in discrete time. Furthermore, when natural enemies are confronted with abundant prey, the predation rate does not increase indefinitely but instead tends to saturate due to the limitation of handling capacity. The Holling II functional response captures this saturation phenomenon in the predation process, which is more consistent with the behavior of natural enemies in actual ecosystems. Based on these, a stochastic discrete pest control model with a Holling II functional response is established, incorporating white noise that affects the growth rate of pest populations and the mortality rate of natural enemy populations. In this paper, we assume that the stochastic variables in the model are independent, doubly truncated stochastic sequences following the standard normal distribution. By constructing auxiliary equations, we prove the positivity and boundedness of the solutions, derive sufficient conditions for pest extinction, and analyze the effects of white noise on population survival and extinction. Numerical simulations are conducted to verify the correctness of the theoretical results and to discuss the effects of key parameters on pest extinction. The results indicate that white noise of relatively low intensity does not alter the survival or extinction of populations, however, if the intensity of white noise affecting a population is too high, it can lead to the extinction of that population. [ABSTRACT FROM AUTHOR]
Copyright of Mathematics & Computers in Simulation is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
An: 192989604
AccessLevel: 6
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PubTypeId: serialPeriodical
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  Label: Title
  Group: Ti
  Data: On the dynamics of a discrete pest-natural enemy model with Holling II response and stochastic perturbations.
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  Data: <searchLink fieldCode="AR" term="%22Liu%2C+Bing%22">Liu, Bing</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> bingliu@mail.asnc.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Zhu%2C+Shimei%22">Zhu, Shimei</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Wen%2C+Buyu%22">Wen, Buyu</searchLink><relatesTo>3</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Qi%2C+Haokun%22">Qi, Haokun</searchLink><relatesTo>1</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Mathematics+%26+Computers+in+Simulation%22">Mathematics & Computers in Simulation</searchLink>. Aug2026, Vol. 246, p477-490. 14p.
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  Data: <searchLink fieldCode="DE" term="%22White+noise%22">White noise</searchLink><br /><searchLink fieldCode="DE" term="%22Stochastic+difference+equations%22">Stochastic difference equations</searchLink><br /><searchLink fieldCode="DE" term="%22Statistical+models%22">Statistical models</searchLink><br /><searchLink fieldCode="DE" term="%22White+noise+theory%22">White noise theory</searchLink><br /><searchLink fieldCode="DE" term="%22Biological+extinction%22">Biological extinction</searchLink><br /><searchLink fieldCode="DE" term="%22Population+dynamics%22">Population dynamics</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+models%22">Mathematical models</searchLink><br /><searchLink fieldCode="DE" term="%22Computer+simulation%22">Computer simulation</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: The survival environment of pests and natural enemies is often subject to various stochastic factors, and the introduction of white noise can better simulate such uncertainty. Compared to continuous models, discrete models are more accurate in describing the situations where the successive generations of many species in nature are non-overlapping and the data of biological samples are usually collected in discrete time. Furthermore, when natural enemies are confronted with abundant prey, the predation rate does not increase indefinitely but instead tends to saturate due to the limitation of handling capacity. The Holling II functional response captures this saturation phenomenon in the predation process, which is more consistent with the behavior of natural enemies in actual ecosystems. Based on these, a stochastic discrete pest control model with a Holling II functional response is established, incorporating white noise that affects the growth rate of pest populations and the mortality rate of natural enemy populations. In this paper, we assume that the stochastic variables in the model are independent, doubly truncated stochastic sequences following the standard normal distribution. By constructing auxiliary equations, we prove the positivity and boundedness of the solutions, derive sufficient conditions for pest extinction, and analyze the effects of white noise on population survival and extinction. Numerical simulations are conducted to verify the correctness of the theoretical results and to discuss the effects of key parameters on pest extinction. The results indicate that white noise of relatively low intensity does not alter the survival or extinction of populations, however, if the intensity of white noise affecting a population is too high, it can lead to the extinction of that population. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Mathematics & Computers in Simulation is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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      – Type: doi
        Value: 10.1016/j.matcom.2026.02.008
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      – Code: eng
        Text: English
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      Pagination:
        PageCount: 14
        StartPage: 477
    Subjects:
      – SubjectFull: White noise
        Type: general
      – SubjectFull: Stochastic difference equations
        Type: general
      – SubjectFull: Statistical models
        Type: general
      – SubjectFull: White noise theory
        Type: general
      – SubjectFull: Biological extinction
        Type: general
      – SubjectFull: Population dynamics
        Type: general
      – SubjectFull: Mathematical models
        Type: general
      – SubjectFull: Computer simulation
        Type: general
    Titles:
      – TitleFull: On the dynamics of a discrete pest-natural enemy model with Holling II response and stochastic perturbations.
        Type: main
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          Name:
            NameFull: Liu, Bing
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            NameFull: Zhu, Shimei
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            NameFull: Wen, Buyu
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            NameFull: Qi, Haokun
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          Dates:
            – D: 01
              M: 08
              Text: Aug2026
              Type: published
              Y: 2026
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              Value: 246
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            – TitleFull: Mathematics & Computers in Simulation
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