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Open AccessArticle

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

by Lina Wang 1, Hui Chang 2,3 and Yuxia Li 2,3,*
1
College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China
2
College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao 266590, China
3
Key Laboratory for Robot and Intelligent Technology of Shandong Province, Shandong University of Science and Technology, Qingdao 266590, China
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(3), 409; https://doi.org/10.3390/math8030409
Received: 20 January 2020 / Revised: 4 March 2020 / Accepted: 9 March 2020 / Published: 12 March 2020
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. View Full-Text
Keywords: fractional-order food-chain system; chaos; bifurcation diagrams; chaotic control; feedback control method; stability margin fractional-order food-chain system; chaos; bifurcation diagrams; chaotic control; feedback control method; stability margin
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Wang, L.; Chang, H.; Li, Y. Dynamics Analysis and Chaotic Control of a Fractional-Order Three-Species Food-Chain System. Mathematics 2020, 8, 409.

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