Complex Dynamics of a Discrete-Time Predator-Prey System with Ivlev Functional Response
Author
Source
Mathematical Problems in Engineering
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-15, 15 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-02-08
Country of Publication
Egypt
No. of Pages
15
Main Subjects
Abstract EN
The dynamics of a discrete-time predator-prey system with Ivlev functional response is investigated in this paper.
The conditions of existence for flip bifurcation and Hopf bifurcation in the interior of R+2 are derived by using the center manifold theorem and bifurcation theory.
Numerical simulations are presented not only to substantiate our theoretical results but also to illustrate the complex dynamical behaviors of the system such as attracting invariant circles, periodic-doubling bifurcation leading to chaos, and periodic-halving phenomena.
In addition, the maximum Lyapunov exponents are numerically calculated to confirm the dynamical complexity of the system.
Finally, we compare the system to discrete systems with Holling-type functional response with respect to dynamical behaviors.
American Psychological Association (APA)
Baek, Hunki. 2018. Complex Dynamics of a Discrete-Time Predator-Prey System with Ivlev Functional Response. Mathematical Problems in Engineering،Vol. 2018, no. 2018, pp.1-15.
https://search.emarefa.net/detail/BIM-1209423
Modern Language Association (MLA)
Baek, Hunki. Complex Dynamics of a Discrete-Time Predator-Prey System with Ivlev Functional Response. Mathematical Problems in Engineering No. 2018 (2018), pp.1-15.
https://search.emarefa.net/detail/BIM-1209423
American Medical Association (AMA)
Baek, Hunki. Complex Dynamics of a Discrete-Time Predator-Prey System with Ivlev Functional Response. Mathematical Problems in Engineering. 2018. Vol. 2018, no. 2018, pp.1-15.
https://search.emarefa.net/detail/BIM-1209423
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1209423