Open AccessChaos in a Financial System with Fractional Order and Its Control via Sliding Mode
Author(s) -
Paul Yaovi Dousseh,
Cyrille Ainamon,
C. H. Miwadinou,
A. V. Monwanou,
J. B. Chabi Orou
Publication year - 2021
Publication title -
complexity
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.447
H-Index - 61
eISSN - 1099-0526
pISSN - 1076-2787
DOI - 10.1155/2021/4636658
Subject(s) - order (exchange) , control theory (sociology) , lyapunov exponent , chaos (operating system) , fractional order system , controller (irrigation) , mode (computer interface) , mathematics , period doubling bifurcation , sliding mode control , control (management) , computer science , nonlinear system , fractional calculus , physics , finance , bifurcation , economics , computer security , quantum mechanics , artificial intelligence , biology , agronomy , operating system
In this paper, the dynamical behaviors and chaos control of a fractional-order financial system are discussed. The lowest fractional order found from which the system generates chaos is 2.49 for the commensurate order case and 2.13 for the incommensurate order case. Also, period-doubling route to chaos was found in this system. The results of this study were validated by the existence of a positive Lyapunov exponent. Besides, in order to control chaos in this fractional-order financial system with uncertain dynamics, a sliding mode controller is derived. The proposed controller stabilizes the commensurate and incommensurate fractional-order systems. Numerical simulations are carried out to verify the analytical results.
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