Impulsive stabilization and synchronization of uncertain financial hyperchaotic systems
Kybernetika, Tome 52 (2016) no. 2, pp. 241-257 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

In this paper the issue of impulsive stabilization and synchronization of uncertain financial hyperchaotic systems with parameters perturbation is investigated. Applying the impulsive control theory, some less conservative and easily verified criteria for the stabilization and synchronization of financial hyperchaotic systems are derived. The control gains and impulsive intervals can be variable. Moreover, the boundaries of the stable region are also estimated according to the equidistant impulse interval. Theoretical analysis and numerical simulations are shown to demonstrate the validity and feasibility of the proposed method.
In this paper the issue of impulsive stabilization and synchronization of uncertain financial hyperchaotic systems with parameters perturbation is investigated. Applying the impulsive control theory, some less conservative and easily verified criteria for the stabilization and synchronization of financial hyperchaotic systems are derived. The control gains and impulsive intervals can be variable. Moreover, the boundaries of the stable region are also estimated according to the equidistant impulse interval. Theoretical analysis and numerical simulations are shown to demonstrate the validity and feasibility of the proposed method.
DOI : 10.14736/kyb-2016-2-0241
Classification : 34C15, 34D06, 34D35
Keywords: financial hyperchaotic system; impulse; stabilization; synchronization
@article{10_14736_kyb_2016_2_0241,
     author = {Zheng, Song},
     title = {Impulsive stabilization and synchronization of uncertain financial hyperchaotic systems},
     journal = {Kybernetika},
     pages = {241--257},
     year = {2016},
     volume = {52},
     number = {2},
     doi = {10.14736/kyb-2016-2-0241},
     mrnumber = {3501160},
     zbl = {1374.34240},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.14736/kyb-2016-2-0241/}
}
TY  - JOUR
AU  - Zheng, Song
TI  - Impulsive stabilization and synchronization of uncertain financial hyperchaotic systems
JO  - Kybernetika
PY  - 2016
SP  - 241
EP  - 257
VL  - 52
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.14736/kyb-2016-2-0241/
DO  - 10.14736/kyb-2016-2-0241
LA  - en
ID  - 10_14736_kyb_2016_2_0241
ER  - 
%0 Journal Article
%A Zheng, Song
%T Impulsive stabilization and synchronization of uncertain financial hyperchaotic systems
%J Kybernetika
%D 2016
%P 241-257
%V 52
%N 2
%U http://geodesic.mathdoc.fr/articles/10.14736/kyb-2016-2-0241/
%R 10.14736/kyb-2016-2-0241
%G en
%F 10_14736_kyb_2016_2_0241
Zheng, Song. Impulsive stabilization and synchronization of uncertain financial hyperchaotic systems. Kybernetika, Tome 52 (2016) no. 2, pp. 241-257. doi: 10.14736/kyb-2016-2-0241

[1] Abd-Elouahab, M., Hamri, N., Wang, J.: Chaos control of a fractional-order financial system. Math. Problems Engrg. 2010 (2010), 1-18. | DOI | Zbl

[2] Agiza, H. N.: Chaos synchronization of Lü dynamical system. Nonlinear Anal. 58 (2004), 11-20. | DOI | MR | Zbl

[3] Cai, G., Yao, L., Hu, P., Fang, X.: Adaptive full state hybrid function projective synchronization of financial hyperchaotic systems with uncertain parameters. Discrete and Continuous Dynamical Systems - Ser. B 18 (2013), 2019-2028. | DOI | MR | Zbl

[4] Cai, G., Zhang, L., Yao., L., Fang, X.: Modified function projective synchronization of financial hyperchaotic systems via adaptive impulsive controller with unknown parameters. Discrete Dynamics in Nature and Society 2015 (2015), 1-11. | DOI

[5] Carroll, T. L., Pecora, L. M.: Synchronizing chaotic circuits. IEEE Trans. Circuits Syst. I 38 (1991), 453-456. | DOI | Zbl

[6] Chen, Y. S., Hwang, R. R., Chang, C. C.: Adaptive impulsive synchronization of uncertain chaotic systems. Phys. Lett. A 374 (2010), 2254-2258. | DOI | Zbl

[7] Deissenberg, C.: Optimal control of linear econometric models with intermittent controls. Econ. Plan. 16 (1980), 49-56. | DOI | Zbl

[8] Ding, J., Yang, W., Yao, H.: A new modified hyperchaotic finance system and its control. Int. J. Nonlinear Sci. 8 (2009), 59-66. | MR | Zbl

[9] Fanti, L., Manfredi, P.: Chaotic business cycles and fiscal policy: an IS-LM model with distributed tax collection lags. Chaos Solitons Fractals 32 (2007), 736-744. | DOI | MR | Zbl

[10] Han, Q. L.: New delay-dependent synchronization criteria for Lur'e systems using time delay feedback control. Phys. Lett. A 360 (2007), 563-569. | DOI | Zbl

[11] Itoh, M., Yang, T., Chua, L. O.: Experimental study of impulsive synchronization of chaotic and hyperchaotic circuits. Int. J. Bifurc. Chaos 9 (1999), 1393-1424. | DOI | Zbl

[12] Itoh, M., Yang, T., L., Chua, O.: Conditions for impulsive synchronization of chaotic and hyperchaotic systems. Int. J. Bifurc. Chaos 11 (2001), 551-560. | DOI | MR

[13] Lakshmikantham, V., Bainov, D. D., Simeonov, P. S.: Theory of Impulsive Differential Equations. World Scientific, Singapore 1989. | DOI | MR | Zbl

[14] Ma, J., Zhang, Q., Gao, Q.: Stability of a three-species symbiosis model with delays. Nonlinear Dynam. 67 (2012), 567-572. | DOI | MR | Zbl

[15] Mainieri, R., Rehacek, J.: Projective synchronization in three-dimensioned chaotic systems. Phys. Rev. Lett. 82 (1999), 3042-3045. | DOI

[16] Nik, H. S., He, P., Talebian, S. T.: Optimal, adaptive and single state feedback control for a 3D chaotic system with golden proportion equilibria. Kybernetika 50 (2014), 596-615. | DOI | MR | Zbl

[17] Park, Ju. H.: Chaos synchronization of a chaotic system via nonlinear control. Chaos Solitons Fractals 25 (2005), 579-584. | DOI | Zbl

[18] Pecora, L. M., Carroll, T. L.: Synchronization in chaotic systems. Phys. Rev. Lett. 64 (1990), 821-824. | DOI | MR | Zbl

[19] Rosenblum, M. G., Pikovsky, A. S., Kurths, J.: Phase synchronization of chaotic oscillators. Phys. Rev. Lett. 76 (1996), 1804-1807. | DOI | Zbl

[20] Sasakura, K.: On the dynamic behavior of Schinasi's business cycle model. J. Macroeconom. 16 (1994), 423-444. | DOI

[21] Strotz, R., McAnulty, J., Naines, J.: Goodwin's nonlinear theory of the business cycle: an electro-analog solution. Econometrica 21 (1953), 390-411. | DOI | Zbl

[22] Wang, Z. L.: Anti-synchronization in two non-identical hyperchaotic systems with known or unknown parameters. Commun. Nonlinear Sci. Numer. Simulat. 14 (2009), 2366-2372. | DOI

[23] Yang, T.: Impulsive Control Theory. Springer-Verlag, Berlin 2001. | DOI | MR | Zbl

[24] Yang, T.: Impulsive control. IEEE Trans. Automat. Control 44 (1999), 1081-1083. | DOI | MR | Zbl

[25] Yang, T., Chua, L. O.: Impulsive stabilization for control and synchronization of chaotic systems: theory and application to secure communication. IEEE Trans. Circuits Syst. I 44 (1997), 976-988. | DOI | MR

[26] Yang, T., Yang, L. B., Yang, C. M.: Impulsive control of Lorenz system. Physica D 110 (1997), 18-24. | DOI | MR | Zbl

[27] Yang, T., Yang, L. B., Yang, C. M.: Impulsive synchronization of Lorenz systems. Phys. Lett. A 226 (1997), 349-354. | DOI

[28] Yu, H., Cai, G., Li, Y.: Dynamic analysis and control of a new hyperchaotic finance system. Nonlinear Dynam. 67 (2012), 2171-2182. | DOI | MR | Zbl

[29] Ma, M., Zhang, H., Cai, J., Zhou, J.: Impulsive practical synchronization of n-dimensional nonautonomous systems. Kybernetika 49 (2013), 539-553. | MR | Zbl

[30] Zhao, M., Wang, J.: $H_\infty$ control of a chaotic finance system in the presence of external disturbance and input time-delay. Appl. Math. Comput. 233 (2014), 320-327. | DOI | MR | Zbl

[31] Zheng, S.: Parameter identification and adaptive impulsive synchronization of uncertain complex-variable chaotic systems. Nonlinear Dynam. 74 (2013), 957-967. | DOI | MR | Zbl

[32] Zheng, J., Du, B.: Projective synchronization of hyperchaotic financial systems. Discrete Dynamics in Nature and Society 2015 (2015), 1-9. | DOI | MR

Cité par Sources :