Complex dynamics and coexistence of period-doubling and period-halving bifurcations in an integrated pest management model with nonlinear impulsive control
Abstract An expectation for optimal integrated pest management is that the instantaneous numbers of natural enemies released should depend on the densities of both pest and natural enemy in the field. For this, a generalised predator–prey model with nonlinear impulsive control tactics is proposed an...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2020-09-01
|
| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-020-02971-9 |
| _version_ | 1818503936166854656 |
|---|---|
| author | Changtong Li Sanyi Tang Robert A. Cheke |
| author_facet | Changtong Li Sanyi Tang Robert A. Cheke |
| author_sort | Changtong Li |
| collection | DOAJ |
| description | Abstract An expectation for optimal integrated pest management is that the instantaneous numbers of natural enemies released should depend on the densities of both pest and natural enemy in the field. For this, a generalised predator–prey model with nonlinear impulsive control tactics is proposed and its dynamics is investigated. The threshold conditions for the global stability of the pest-free periodic solution are obtained based on the Floquet theorem and analytic methods. Also, the sufficient conditions for permanence are given. Additionally, the problem of finding a nontrivial periodic solution is confirmed by showing the existence of a nontrivial fixed point of the model’s stroboscopic map determined by a time snapshot equal to the common impulsive period. In order to address the effects of nonlinear pulse control on the dynamics and success of pest control, a predator–prey model incorporating the Holling type II functional response function as an example is investigated. Finally, numerical simulations show that the proposed model has very complex dynamical behaviour, including period-doubling bifurcation, chaotic solutions, chaos crisis, period-halving bifurcations and periodic windows. Moreover, there exists an interesting phenomenon whereby period-doubling bifurcation and period-halving bifurcation always coexist when nonlinear impulsive controls are adopted, which makes the dynamical behaviour of the model more complicated, resulting in difficulties when designing successful pest control strategies. |
| first_indexed | 2024-12-10T21:30:27Z |
| format | Article |
| id | doaj.art-32854bd133204637820ed01f39ea75ee |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-10T21:30:27Z |
| publishDate | 2020-09-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-32854bd133204637820ed01f39ea75ee2022-12-22T01:32:49ZengSpringerOpenAdvances in Difference Equations1687-18472020-09-012020112310.1186/s13662-020-02971-9Complex dynamics and coexistence of period-doubling and period-halving bifurcations in an integrated pest management model with nonlinear impulsive controlChangtong Li0Sanyi Tang1Robert A. Cheke2School of Science, Xi’an Technological UniversitySchool of Mathematics and Information Science, Shaanxi Normal UniversityNatural Resources Institute, University of Greenwich at MedwayAbstract An expectation for optimal integrated pest management is that the instantaneous numbers of natural enemies released should depend on the densities of both pest and natural enemy in the field. For this, a generalised predator–prey model with nonlinear impulsive control tactics is proposed and its dynamics is investigated. The threshold conditions for the global stability of the pest-free periodic solution are obtained based on the Floquet theorem and analytic methods. Also, the sufficient conditions for permanence are given. Additionally, the problem of finding a nontrivial periodic solution is confirmed by showing the existence of a nontrivial fixed point of the model’s stroboscopic map determined by a time snapshot equal to the common impulsive period. In order to address the effects of nonlinear pulse control on the dynamics and success of pest control, a predator–prey model incorporating the Holling type II functional response function as an example is investigated. Finally, numerical simulations show that the proposed model has very complex dynamical behaviour, including period-doubling bifurcation, chaotic solutions, chaos crisis, period-halving bifurcations and periodic windows. Moreover, there exists an interesting phenomenon whereby period-doubling bifurcation and period-halving bifurcation always coexist when nonlinear impulsive controls are adopted, which makes the dynamical behaviour of the model more complicated, resulting in difficulties when designing successful pest control strategies.http://link.springer.com/article/10.1186/s13662-020-02971-9Nonlinear impulsiveThreshold conditionBifurcationNontrivial periodic solutionChaos |
| spellingShingle | Changtong Li Sanyi Tang Robert A. Cheke Complex dynamics and coexistence of period-doubling and period-halving bifurcations in an integrated pest management model with nonlinear impulsive control Advances in Difference Equations Nonlinear impulsive Threshold condition Bifurcation Nontrivial periodic solution Chaos |
| title | Complex dynamics and coexistence of period-doubling and period-halving bifurcations in an integrated pest management model with nonlinear impulsive control |
| title_full | Complex dynamics and coexistence of period-doubling and period-halving bifurcations in an integrated pest management model with nonlinear impulsive control |
| title_fullStr | Complex dynamics and coexistence of period-doubling and period-halving bifurcations in an integrated pest management model with nonlinear impulsive control |
| title_full_unstemmed | Complex dynamics and coexistence of period-doubling and period-halving bifurcations in an integrated pest management model with nonlinear impulsive control |
| title_short | Complex dynamics and coexistence of period-doubling and period-halving bifurcations in an integrated pest management model with nonlinear impulsive control |
| title_sort | complex dynamics and coexistence of period doubling and period halving bifurcations in an integrated pest management model with nonlinear impulsive control |
| topic | Nonlinear impulsive Threshold condition Bifurcation Nontrivial periodic solution Chaos |
| url | http://link.springer.com/article/10.1186/s13662-020-02971-9 |
| work_keys_str_mv | AT changtongli complexdynamicsandcoexistenceofperioddoublingandperiodhalvingbifurcationsinanintegratedpestmanagementmodelwithnonlinearimpulsivecontrol AT sanyitang complexdynamicsandcoexistenceofperioddoublingandperiodhalvingbifurcationsinanintegratedpestmanagementmodelwithnonlinearimpulsivecontrol AT robertacheke complexdynamicsandcoexistenceofperioddoublingandperiodhalvingbifurcationsinanintegratedpestmanagementmodelwithnonlinearimpulsivecontrol |