Submitted:
03 April 2018
Posted:
10 April 2018
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Abstract
This paper first discusses a fractional-order Liu system of order as low as 2.7 and shows its chaotic characteristics by carrying out numerical simulations such as Lyapunov exponents, bifurcation diagrams and phase portraits. Then, by using the topological horseshoe theory and computer-assisted proof, the existence of chaos in the system is verified theoretically. Finally, the fractional-order system is implemented on a Field Programmable Gate Array (FPGA) and the results obtained show that the fractional-order Liu system is indeed chaotic.
Keywords:
Topological-entropy
; Chaos
; Fractional-order
; Computer-assisted proof
; Topological Horseshoe Analysis
; FPGA
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