Chaos Control of a Fractional-Order Financial System
By Mohammed Salah Abdelouahab, Nasr-eddine Hamri, Junwei Wang. 2010
83 citations recorded by the source corpus.
Fractional-order financial system introduced by W.-C. Chen (2008) displays chaotic motions at order less than 3. In this paper we have extended the nonlinear feedback control in ODE systems to fractional-order systems, in order to eliminate the chaotic behavior. The results are proved analytically by applying the Lyapunov linearization method and stability condition for fractional system. Moreover numerical simulations are shown to verify the effectiveness of the proposed control scheme.
Subfields: Modeling and Simulation, Public Health, Environmental and Occupational Health, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/0db583f62a3f1c175028fdab28b803e998ac1983
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In Modeling and Simulation
- Eva Kaslik
- Seenith Sivasundaram
- Xia Huang
- Guodong Shi
- Zhen Wang
- Mohammed Salah Abdelouahab
- Nasr-eddine Hamri
In Public Health, Environmental and Occupational Health
In Statistical and Nonlinear Physics
Citations in the corpus
- Analysis of nonlinear dynamics and chaos in a fractional order financial system with time delay (2011, methodology): “[20,21] studied the chaos control method of such a kind of system by slide mode and feedback control, respectively.”
- The Grünwald–Letnikov Fractional-Order Derivative with Fixed Memory Length (2013, background): “In chaos theory, the idea of chaos control is based on the fact that chaotic attractors have a skeleton made of an infinite number of unstable periodic orbits which are subjected for stabilization [14–16].”
- Non-existence of periodic solutions in fractional-order dynamical systems and a remarkable difference between integer and fractional-order derivatives of periodic functions☆ (2011, methodology): “Even though, based on Corollary 3, exact periodic solutions do not exist in autonomous fractional-order systems, oscillatory behavior (limit cycles) has been observed by numerical simulations in many systems such as: a fractional-order Van der Pol system [6], fractional-order Chua and Chen’s systems”