Dynamics Analysis and Chaotic Control of a Fractional-Order Three-Species Food-Chain System

Lina Wang, Hui Chang and Yuxia Li
Additional contact information
Lina Wang: College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China
Hui Chang: College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao 266590, China
Yuxia Li: College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao 266590, China

Mathematics, 2020, vol. 8, issue 3, 1-15

Abstract: Based on Hastings and Powell’s research, this paper extends a three-species food-chain system to fractional-order form, whose dynamics are analyzed and explored. The necessary conditions for generating chaos are confirmed by the stability theory of fractional-order systems, chaos is characterized by its phase diagrams, and bifurcation diagrams prove that the dynamic behaviors of the fractional-order food-chain system are affected by the order. Next, the chaotic control of the fractional-order system is realized by the feedback control method with a good effect in a relative short period. The stability margin of the controlled system is revealed by the theory and numerical analysis. Finally, the results of theory analysis are verified by numerical simulations.

Keywords: fractional-order food-chain system; chaos; bifurcation diagrams; chaotic control; feedback control method; stability margin (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.mdpi.com/2227-7390/8/3/409/pdf (application/pdf)
https://www.mdpi.com/2227-7390/8/3/409/ (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:8:y:2020:i:3:p:409-:d:331855

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 ().