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10.3390/math8030409
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Article

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
Submission received: 20 January 2020 / Revised: 4 March 2020 / Accepted: 9 March 2020 / Published: 12 March 2020
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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 fractional-order food-chain system; chaos; bifurcation diagrams; chaotic control; feedback control method; stability margin

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MDPI and ACS Style

Wang, L.; Chang, H.; Li, Y. Dynamics Analysis and Chaotic Control of a Fractional-Order Three-Species Food-Chain System. Mathematics 2020, 8, 409. https://doi.org/10.3390/math8030409

AMA Style

Wang L, Chang H, Li Y. Dynamics Analysis and Chaotic Control of a Fractional-Order Three-Species Food-Chain System. Mathematics. 2020; 8(3):409. https://doi.org/10.3390/math8030409

Chicago/Turabian Style

Wang, Lina, Hui Chang, and Yuxia Li. 2020. "Dynamics Analysis and Chaotic Control of a Fractional-Order Three-Species Food-Chain System" Mathematics 8, no. 3: 409. https://doi.org/10.3390/math8030409

APA Style

Wang, L., Chang, H., & Li, Y. (2020). Dynamics Analysis and Chaotic Control of a Fractional-Order Three-Species Food-Chain System. Mathematics, 8(3), 409. https://doi.org/10.3390/math8030409

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