The dynamical behaviors of a Ivlev-type two-prey two-predator system with impulsive effect

Xingjie Wu (), Wei Du, Genan Pan and Wentao Huang
Additional contact information
Xingjie Wu: Hefei Normal University
Wei Du: Huainan Normal University
Genan Pan: Hefei Normal University
Wentao Huang: Guilin University of Electronic Technology

Indian Journal of Pure and Applied Mathematics, 2013, vol. 44, issue 1, 1-27

Abstract: Abstract In this paper, considering the strategy of integrated Pest Management (IPM), a class of two-prey two-predator system with the Ivlev-type functional response and impulsive effect at different fixed time is established. By using impulsive comparison theorem, Floquent theory and small amplitude perturbation skill, the sufficient conditions for the system to be extinct of prey and permanence are proved. Moreover, we give two sufficient conditions for the extinction of one of two prey and remaining three species are permanent. Numerical simulation shows that there exist complex dynamics for system, such as symmetry-breaking pitchfork bifurcation, periodic doubling bifurcation, chaos, periodic halving cascade. Lastly, a brief discussion is given.

Keywords: Prey-predator; impulsive differential system; impulsive comparison theorem; chaos; integrated pest management (search for similar items in EconPapers)
Date: 2013
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s13226-013-0001-3 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

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:spr:indpam:v:44:y:2013:i:1:d:10.1007_s13226-013-0001-3

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/13226

DOI: 10.1007/s13226-013-0001-3

Access Statistics for this article

Indian Journal of Pure and Applied Mathematics is currently edited by Nidhi Chandhoke

More articles in Indian Journal of Pure and Applied Mathematics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().