Chaos in a Financial System with Fractional Order and Its Control via Sliding Mode

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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Corrigendum to “Chaos in a Financial System with Fractional Order and Its Control via Sliding Mode”

Complexity ◽

10.1155/2021/9789470 ◽

2021 ◽

Vol 2021 ◽

pp. 1-16

Author(s):

Paul Yaovi Dousseh ◽

Cyrille Ainamon ◽

Clément Hodévèwan Miwadinou ◽

Adjimon Vincent Monwanou ◽

Jean Bio Chabi Orou

Keyword(s):

Fractional Order ◽

Chaos Control ◽

Sliding Mode ◽

Financial System ◽

Period Doubling ◽

Fractional Order Systems ◽

Uncertain Dynamics ◽

Dynamical Behaviors ◽

Order Case ◽

Route To Chaos

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 2.57 for the incommensurate order case. Also, the 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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Dynamic Analysis and Adaptive Sliding Mode Controller for a Chaotic Fractional Incommensurate Order Financial System

International Journal of Bifurcation and Chaos ◽

10.1142/s021812741750198x ◽

2017 ◽

Vol 27 (13) ◽

pp. 1750198 ◽

Cited By ~ 9

Author(s):

Ahmad Hajipour ◽

Hamidreza Tavakoli

Keyword(s):

Control Method ◽

Sliding Mode ◽

Financial System ◽

Period Doubling ◽

Largest Lyapunov Exponent ◽

Sliding Mode Controller ◽

Adaptive Sliding Mode Controller ◽

Uncertain Dynamics ◽

Route To Chaos ◽

Doubling Sequence

In this study, the dynamic behavior and chaos control of a chaotic fractional incommensurate-order financial system are investigated. Using well-known tools of nonlinear theory, i.e. Lyapunov exponents, phase diagrams and bifurcation diagrams, we observe some interesting phenomena, e.g. antimonotonicity, crisis phenomena and route to chaos through a period doubling sequence. Adopting largest Lyapunov exponent criteria, we find that the system yields chaos at the lowest order of [Formula: see text]. Next, in order to globally stabilize the chaotic fractional incommensurate order financial system with uncertain dynamics, an adaptive fractional sliding mode controller is designed. Numerical simulations are used to demonstrate the effectiveness of the proposed control method.

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CHAOS AND ADAPTIVE SYNCHRONIZATIONS IN FRACTIONAL-ORDER SYSTEMS

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127413501757 ◽

2013 ◽

Vol 23 (11) ◽

pp. 1350175 ◽

Cited By ~ 5

Author(s):

XIAOJUN LIU ◽

LING HONG

Keyword(s):

Fractional Order ◽

Period Doubling ◽

Adaptive Synchronization ◽

Fractional Order Systems ◽

Effective Dimension ◽

Unknown Parameters ◽

Order Case ◽

The Stability ◽

Fifth Order ◽

Derivative Order

In this paper, chaos and adaptive synchronization for a fractional-order Genesio–Tesi system with fifth order nonlinearity are investigated. The minimum effective dimension for the system to remain chaotic is 2.784 in the commensurate-order case and 2.793 in the incommensurate-order case. A period-doubling bifurcation and an interior crisis from single-scroll to double-scroll attractors are also found with the variation of derivative order. Furthermore, based on the stability theory of fractional-order systems, the adaptive synchronization of the system with unknown parameters is realized by designing appropriated controllers. Numerical simulations are carried out to demonstrate the effectiveness and flexibility of the controllers.

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