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Number of results

Journal

2013 | 11 | 6 | 824-835

Article title

Synchronization of variable-order fractional financial system via active control method

Authors

Content

Title variants

Languages of publication

EN

Abstracts

EN
In this paper, we study the chaotic dynamics of a Variable-Order Fractional Financial System (VOFFS). The Variable-Order Fractional Derivative (VOFD) is defined in Caputo type. A necessary condition for occurrence of chaos in VOFFS is obtained. Numerical experiments on the dynamics of the VOFFS with various conditions are given. Based on them, it is shown that the VOFFS has complex dynamical behavior, and the occurrence of chaos depends on the choice of order function. Furthermore, the chaos synchronization of the VOFFS is studied via active control method. Numerical simulations demonstrate that the active control method is effective and simple for synchronizing the VOFFSs with commensurate or incommensurate order functions.

Publisher

Journal

Year

Volume

11

Issue

6

Pages

824-835

Physical description

Dates

published
1 - 6 - 2013
online
9 - 10 - 2013

Contributors

author
  • Department of Applied Mathematics, School of Mathematics and Statistics, Central South University, Hunan, 410083, Changsha, People’s Republic of China
author
  • Department of Applied Mathematics, School of Mathematics and Statistics, Central South University, Hunan, 410083, Changsha, People’s Republic of China

References

  • [1] L. Pecora, T. Carroll, Phys. Rev. Lett. 64, 8 (1990) http://dx.doi.org/10.1103/PhysRevLett.64.821[Crossref]
  • [2] M. Faieghi, H. Delavari, Commun. Nonlinear Sci. Numer. Simulat. 17, 2 (2012)
  • [3] B. Blasius, A. Huppert, L. Stone, Nature, 399 (1999)
  • [4] C. Ahn, Nonlinear Anal. Hybrid Syst. 9, 1 (2013) http://dx.doi.org/10.1016/j.nahs.2013.01.002[Crossref]
  • [5] Z. Ge, J. Lee, Appl. Math. Comput. 163, 2 (2005) http://dx.doi.org/10.1016/j.amc.2004.04.008[Crossref]
  • [6] H. Haken, Physica D, 205, 1 (2005) http://dx.doi.org/10.1016/j.physd.2005.04.010[Crossref]
  • [7] L. Kocarev et. al., Int. J. Bifurcation Chaos 2, 709 (1992) http://dx.doi.org/10.1142/S0218127492000823[Crossref]
  • [8] C. Ahn, Nonlinear Dyn. 60, 3 (2010)
  • [9] I. Podlubny, Fractional Differential Equations (Academic Press, San Diego, CA, 1999)
  • [10] A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations (Elsevier Science B. V., Amsterdam, 2006)
  • [11] K. Diethelm, The Analysis of Fractional Differential Equations (Springer-Verlag, Berlin Heidelberg, 2010) http://dx.doi.org/10.1007/978-3-642-14574-2[Crossref]
  • [12] I. Petráš, Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation (Springer-Verlag, Berlin Heidelberg, 2011) http://dx.doi.org/10.1007/978-3-642-18101-6[Crossref]
  • [13] Y. Xu, Z. He, Comput. Math. Appl. 62, 12 (2011)
  • [14] R. Hilfer, Physica A. 329, 1 (2003) http://dx.doi.org/10.1016/S0378-4371(03)00594-6[Crossref]
  • [15] S. Müller, M. Kästner, J. Brummund, V. Ulbricht, Comput. Mater. Sci. 50, 10 (2011) http://dx.doi.org/10.1016/j.commatsci.2011.05.011[Crossref]
  • [16] O. Heaviside, Electromagnetic Theory (Chelsea, New York, 1971)
  • [17] N. Laskin, Physica A. 287, 3 (2000) http://dx.doi.org/10.1016/S0378-4371(00)00387-3[Crossref]
  • [18] D. Kunsezov, A. Bulagc, G. D. Dang, Phys. Rev. Lett. 82, 6 (1999) http://dx.doi.org/10.1103/PhysRevLett.82.6[Crossref]
  • [19] I. Gupalo, V. Novikov, I. Riazantsev, J. Appl. Math. Mech. 45, 2 (1981) http://dx.doi.org/10.1016/0021-8928(81)90037-X[Crossref]
  • [20] R. Magin, Comput. Math. Appl. 59, 5 (2010) http://dx.doi.org/10.1016/j.camwa.2009.08.039[Crossref]
  • [21] H. G. Sun, W. Chen, Y. Q. Chen, Physica A 388, 21 (2009) http://dx.doi.org/10.1016/j.physa.2008.09.030[Crossref]
  • [22] S. Samko, Anal. Math. 21, 1995 (1995) http://dx.doi.org/10.1007/BF01911126[Crossref]
  • [23] Y. Xu, Z. He, J. Appl. Math. 2013, 2013 (2013) (in press)
  • [24] H. Sheng, H. G. Sun, C. Coopmans, Y. Q. Chen, G. W. Bohannan, Eur. Phys. J. 193, 2011 (2011)
  • [25] C. Coimbra, Ann. Phys. 12, 11 (2003) http://dx.doi.org/10.1002/andp.200310032[Crossref]
  • [26] G. Cooper, D. R. Cowan, Comput. Geosci. 30, 5 (2004) http://dx.doi.org/10.1016/j.cageo.2003.08.009[Crossref]
  • [27] C. C. Tseng, Signal Proc. 86, 10 (2006)
  • [28] H. Sheng, H. G. Sun, Y. Q. Chen, T. S. Qiu, Signal Proc. 91, 7 (2011)
  • [29] M. Aghababa, Commun. Nonlinear Sci. Numer. Simulat. 17, 6 (2012)
  • [30] J. Bai, Y. G. Yu, S. Wang, Y. Song, Commun. Nonlinear Sci. Numer. Simulat. 17, 4 (2012)
  • [31] C. Ahn, Prog. Theoret. Phys. 123, 3 (2010)
  • [32] C. Ahn, Nonlinear Dyn. 59, 319 (2010) http://dx.doi.org/10.1007/s11071-009-9541-9[Crossref]
  • [33] S. Bhalekar, V. Daftardar-Gejji, Commun. Nonlinear Sci. Numer. Simulat. 15, 11 (2010)
  • [34] S. Kuntanapreeda, Comput. Math. Appl. 63, 1 (2012) http://dx.doi.org/10.1016/j.camwa.2011.09.022[Crossref]
  • [35] S. Ma, Y. Xu, W. Yue, J. Appl. Math. 2012, 2012 (2012)
  • [36] D. Matignon, Computational Engineering in Systems and Application multi-conference, vol. 2, IMACS, In: IEEE-SMC Proceedings, Lille, France, July 1996, pp. 963–968
  • [37] W. Chen, Chaos Soliton Fractal. 36, 5 (2008)
  • [38] X. Y. Wang, J. M. Song, Commun. Nonlinear Sci. Numer. Simulat. 14, 8 (2009)
  • [39] V. Daftardar-Gejji, S. Bhalekar, Comput. Math. Appl. 59, 3 (2010)

Document Type

Publication order reference

Identifiers

YADDA identifier

bwmeta1.element.-psjd-doi-10_2478_s11534-013-0237-x
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