Abstract
Synchronization of fractional order chaotic dynamical systems is receiving increasing attention in recent decades. In this article, a fractional-order financial system is proposed and we utilize active control technique to synchronize this fractional order chaotic dynamical system based on the stability theory of fractional order systems. It is observed that synchronization is faster as the order tends to one. Finally, the numerical simulations are given to verify the feasibility of the results.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Hilfer, R.: Applications of fractional calculus in physics. World Scientific, USA (2001)
He, R., Vaidya, P.G.: Implementation of chaotic cryptography with chaotic synchronization. Phys. Rev. EÂ 57(2), 1532 (1998)
Huang, L., Feng, R., Wang, M.: Synchronization of chaotic systems via nonlinear control. Phys. Lett. AÂ 320, 271 (2004)
Park, J.H.: Adaptive synchronization of Rossler system with uncertain parameters. Chaos Solitons Fractals 25, 333–338 (2005)
Bowong, S., Moukam Kakmeni, F.: Synchronization of uncertain chaotic systems via backstepping approach. Chaos Solitons Fractals 21, 999–1011 (2004)
Shahiri, M., Ghaderi, R., Ranjbar, A., Hosseinnia, S.H., Momani, S.: Chaotic fractional-order Coullet system: synchronization and control approach. Commun. Nonlinear Sci. Numer. Simulat. 15, 665–674 (2010)
Tavazoei, M.S., Haeri, M.: A necessary condition for double scroll attractor existence in fractional-order systems. Ameria: Physics Letters A 367, 102–113 (2007)
Diethelm, K., Ford, N.J., Freed, A.D.: A predictor–corrector approach for the numerical solution of fractional differential equations. Nonlinear Dynam. 29, 3–22 (2002)
Diethelm, K.: An algorithm for the numerical solution of differential equations of fractional order. Electron. Trans. Numer. Anal. 5, 1–6 (1997)
Diethelm, K., Ford, N.J.: Analysis of fractional differential equations. J. Math. Anal. Appl. 265, 229–248 (2002)
Matignon, D.: Stability results for fractional differential equations with application to control processing. Computational Engineering System Application 2, 963–968 (1996)
Mohammad, S.T., Mohammad, H.: A note on the stability of fractional order systems. Math. Comput. Simulat. (2007)
Wang, X.Y., Song, J.M.: Synchronization of the fractional order hyperchaos Lorenz systems with activation feedback control. Commun. Nonlinear Sci. Numer. Simulat. 14, 3351–3357 (2009)
Chen, W.C.: Nonlinear dynamics and chaos in a fractional-order financial system. Chaos Solitons and Fractals 36, 1305–1314 (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Wang, Y., Zhang, C. (2011). Synchronization of the Fractional Order Finance Systems with Activation Feedback Control. In: Deng, H., Miao, D., Lei, J., Wang, F.L. (eds) Artificial Intelligence and Computational Intelligence. AICI 2011. Lecture Notes in Computer Science(), vol 7002. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23881-9_16
Download citation
DOI: https://doi.org/10.1007/978-3-642-23881-9_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-23880-2
Online ISBN: 978-3-642-23881-9
eBook Packages: Computer ScienceComputer Science (R0)