Impulsive Effects and Complexity Dynamics in the Anti-Predator Model with IPM Strategies

Wenjie Qin, Zhengjun Dong and Lidong Huang ()
Additional contact information
Wenjie Qin: Department of Mathematics, Yunnan Minzu University, Kunming 650500, China
Zhengjun Dong: Department of Mathematics, Yunnan Minzu University, Kunming 650500, China
Lidong Huang: Department of Mathematics, Yunnan Minzu University, Kunming 650500, China

Mathematics, 2024, vol. 12, issue 7, 1-25

Abstract: When confronted with the imminent threat of predation, the prey instinctively employ strategies to avoid being consumed. These anti-predator tactics involve individuals acting collectively to intimidate predators and reduce potential harm during an attack. In the present work, we propose a state-dependent feedback control predator-prey model that incorporates a nonmonotonic functional response, taking into account the anti-predator behavior observed in pest-natural enemy ecosystems within the agricultural context. The qualitative analysis of this model is presented utilizing the principles of impulsive semi-dynamical systems. Firstly, the stability conditions of the equilibria are derived by employing pertinent properties of planar systems. The precise domain of the impulsive set and phase set is determined by considering the phase portrait of the system. Secondly, a Poincaré map is constructed by utilizing the sequence of impulsive points within the phase set. The stability of the order-1 periodic solution at the boundary is subsequently analyzed by an analog of the Poincaré criterion. Additionally, this article presents various threshold conditions that determine both the existence and stability of an order-1 periodic solution. Furthermore, it investigates the existence of order- k ( k ≥ 2 ) periodic solutions. Finally, the article explores the complex dynamics of the model, encompassing multiple bifurcation phenomena and chaos, through computational simulations.

Keywords: impulsive semi-dynamics system; bifurcation analysis; anti-predator behavior; order- k periodic solution; chaos (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/7/1043/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/7/1043/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:7:p:1043-:d:1367641

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().