Global Dynamics of the Hastings-Powell System
Author
Source
Mathematical Problems in Engineering
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-8, 8 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-12-17
Country of Publication
Egypt
No. of Pages
8
Main Subjects
Abstract EN
This paper studies the problem of bounding a domain that contains all compact invariant sets of the Hastings-Powell system.
The results were obtained using the first-order extremum conditions and the iterative theorem to a biologically meaningful model.
As a result, we calculate the bounds given by a tetrahedron with excisions, described by several inequalities of the state variables and system parameters.
Therefore, a region is identified where all the system dynamics are located, that is, its compact invariant sets: equilibrium points, periodic-homoclinic-heteroclinic orbits, and chaotic attractors.
It was also possible to formulate a nonexistence condition of the compact invariant sets.
Additionally, numerical simulations provide examples of the calculated boundaries for the chaotic attractors or periodic orbits.
The results provide insights regarding the global dynamics of the system.
American Psychological Association (APA)
Coria, Luis N.. 2013. Global Dynamics of the Hastings-Powell System. Mathematical Problems in Engineering،Vol. 2013, no. 2013, pp.1-8.
https://search.emarefa.net/detail/BIM-1009483
Modern Language Association (MLA)
Coria, Luis N.. Global Dynamics of the Hastings-Powell System. Mathematical Problems in Engineering No. 2013 (2013), pp.1-8.
https://search.emarefa.net/detail/BIM-1009483
American Medical Association (AMA)
Coria, Luis N.. Global Dynamics of the Hastings-Powell System. Mathematical Problems in Engineering. 2013. Vol. 2013, no. 2013, pp.1-8.
https://search.emarefa.net/detail/BIM-1009483
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1009483