chaotic control
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Author(s):  
Wafa’ Hamdan Alshoura ◽  
Zurinahni Zainol ◽  
Je Sen Teh ◽  
Moatsum Alawida

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 409 ◽  
Author(s):  
Lina Wang ◽  
Hui Chang ◽  
Yuxia Li

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.


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