Dynamic complexity of a predator-prey model for IPM with nonlinear impulsive control incorporating a regulatory factor for predator releases
The success of integrated pest management (IPM) depends on spraying the correct amount of pesticides at an appropriate time and releases of natural enemies or pathogens of the pest in appropriate proportions at critical times, with little cost and minimal effects on the environment. Therefore, contr...
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| Format: | Article |
| Language: | English |
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Vilnius Gediminas Technical University
2019-01-01
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| Series: | Mathematical Modelling and Analysis |
| Subjects: | |
| Online Access: | https://journals.vgtu.lt/index.php/MMA/article/view/2196 |
| _version_ | 1818788684121505792 |
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| author | Yuan Tian Sanyi Tang Robert A. Cheke |
| author_facet | Yuan Tian Sanyi Tang Robert A. Cheke |
| author_sort | Yuan Tian |
| collection | DOAJ |
| description | The success of integrated pest management (IPM) depends on spraying the correct amount of pesticides at an appropriate time and releases of natural enemies or pathogens of the pest in appropriate proportions at critical times, with little cost and minimal effects on the environment. Therefore, control decisions require information on instantaneous killing rates of pesticides and numbers of natural enemies to be released, variables that should depend on the densities of both pest and natural enemy population densities in the field. To describe such a control strategy we have proposed a mathematical model of IPM involving releases of natural enemies in relation to a regulatory factor. The threshold condition for the existence and stability of the pest free periodic solution is provided using a cobweb model, the comparison principle and Floquet theory, which reveals the effects of nonlinear control actions on pest outbreaks. Bifurcation analyses show that the dynamics of the proposed model can be very complex, including multiple attractors and switch-like transition patterns following small random perturbations. Moreover, the random perturbations and nonlinear impulsive control measures could generate complex switching patterns, which show that the pest population could have outbreaks in complex ways due to environmental noise. |
| first_indexed | 2024-12-18T14:27:34Z |
| format | Article |
| id | doaj.art-6b228ac7909f44bda6a3dc66bb0ab2c1 |
| institution | Directory Open Access Journal |
| issn | 1392-6292 1648-3510 |
| language | English |
| last_indexed | 2024-12-18T14:27:34Z |
| publishDate | 2019-01-01 |
| publisher | Vilnius Gediminas Technical University |
| record_format | Article |
| series | Mathematical Modelling and Analysis |
| spelling | doaj.art-6b228ac7909f44bda6a3dc66bb0ab2c12022-12-21T21:04:41ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102019-01-0124110.3846/mma.2019.010Dynamic complexity of a predator-prey model for IPM with nonlinear impulsive control incorporating a regulatory factor for predator releasesYuan Tian0Sanyi Tang1Robert A. Cheke2School of Mathematics and Information Science, Shaanxi Normal University, Xi’an, 710062, China; School of Science, Hubei University For Nationalities, Enshi, 445000, ChinaSchool of Mathematics and Information Science, Shaanxi Normal University, Xi’an, 710062, ChinaNatural Resources Institute, University of Greenwich at Medway, Central Avenue, Chatham Maritime, Chatham, Kent, ME4 4TB, UKThe success of integrated pest management (IPM) depends on spraying the correct amount of pesticides at an appropriate time and releases of natural enemies or pathogens of the pest in appropriate proportions at critical times, with little cost and minimal effects on the environment. Therefore, control decisions require information on instantaneous killing rates of pesticides and numbers of natural enemies to be released, variables that should depend on the densities of both pest and natural enemy population densities in the field. To describe such a control strategy we have proposed a mathematical model of IPM involving releases of natural enemies in relation to a regulatory factor. The threshold condition for the existence and stability of the pest free periodic solution is provided using a cobweb model, the comparison principle and Floquet theory, which reveals the effects of nonlinear control actions on pest outbreaks. Bifurcation analyses show that the dynamics of the proposed model can be very complex, including multiple attractors and switch-like transition patterns following small random perturbations. Moreover, the random perturbations and nonlinear impulsive control measures could generate complex switching patterns, which show that the pest population could have outbreaks in complex ways due to environmental noise.https://journals.vgtu.lt/index.php/MMA/article/view/2196IPMnonlinear control actionpest free periodic solutionswitch-like transitionrandom perturbation |
| spellingShingle | Yuan Tian Sanyi Tang Robert A. Cheke Dynamic complexity of a predator-prey model for IPM with nonlinear impulsive control incorporating a regulatory factor for predator releases Mathematical Modelling and Analysis IPM nonlinear control action pest free periodic solution switch-like transition random perturbation |
| title | Dynamic complexity of a predator-prey model for IPM with nonlinear impulsive control incorporating a regulatory factor for predator releases |
| title_full | Dynamic complexity of a predator-prey model for IPM with nonlinear impulsive control incorporating a regulatory factor for predator releases |
| title_fullStr | Dynamic complexity of a predator-prey model for IPM with nonlinear impulsive control incorporating a regulatory factor for predator releases |
| title_full_unstemmed | Dynamic complexity of a predator-prey model for IPM with nonlinear impulsive control incorporating a regulatory factor for predator releases |
| title_short | Dynamic complexity of a predator-prey model for IPM with nonlinear impulsive control incorporating a regulatory factor for predator releases |
| title_sort | dynamic complexity of a predator prey model for ipm with nonlinear impulsive control incorporating a regulatory factor for predator releases |
| topic | IPM nonlinear control action pest free periodic solution switch-like transition random perturbation |
| url | https://journals.vgtu.lt/index.php/MMA/article/view/2196 |
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