Article
Full entry |
PDF
(0.9 MB)
Feedback
PDF
(0.9 MB)
Feedback
Keywords:
financial hyperchaotic system; impulse; stabilization; synchronization
financial hyperchaotic system; impulse; stabilization; synchronization
Summary:
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.
References:
[1] Abd-Elouahab, M., Hamri, N., Wang, J.: Chaos control of a fractional-order financial system. Math. Problems Engrg. 2010 (2010), 1-18. DOI 10.1155/2010/270646 | Zbl 1195.91185
[2] Agiza, H. N.: Chaos synchronization of Lü dynamical system. Nonlinear Anal. 58 (2004), 11-20. DOI 10.1016/j.na.2004.04.002 | MR 2070803 | Zbl 1057.34042
[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 10.3934/dcdsb.2013.18.2019 | MR 3082308 | Zbl 1283.34051
[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 10.1155/2015/572735
[5] Carroll, T. L., Pecora, L. M.: Synchronizing chaotic circuits. IEEE Trans. Circuits Syst. I 38 (1991), 453-456. DOI 10.1109/31.75404 | Zbl 1058.37538
[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 10.1016/j.physleta.2010.03.046 | Zbl 1237.34099
[7] Deissenberg, C.: Optimal control of linear econometric models with intermittent controls. Econ. Plan. 16 (1980), 49-56. DOI 10.1007/bf00351465 | Zbl 0466.90018
[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 2557980 | Zbl 1179.37124
[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 10.1016/j.chaos.2005.11.024 | MR 2280116 | Zbl 1133.91482
[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 10.1016/j.physleta.2006.08.076 | Zbl 1236.93072
[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 10.1142/s0218127499000961 | Zbl 0963.34029
[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 10.1142/s0218127401002262 | MR 1830352
[13] Lakshmikantham, V., Bainov, D. D., Simeonov, P. S.: Theory of Impulsive Differential Equations. World Scientific, Singapore 1989. DOI 10.1142/0906 | MR 1082551 | Zbl 0719.34002
[14] Ma, J., Zhang, Q., Gao, Q.: Stability of a three-species symbiosis model with delays. Nonlinear Dynam. 67 (2012), 567-572. DOI 10.1007/s11071-011-0009-3 | MR 2869224 | Zbl 1242.92059
[15] Mainieri, R., Rehacek, J.: Projective synchronization in three-dimensioned chaotic systems. Phys. Rev. Lett. 82 (1999), 3042-3045. DOI 10.1103/physrevlett.82.3042
[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 10.14736/kyb-2014-4-0596 | MR 3275087 | Zbl 1310.34089
[17] Park, Ju. H.: Chaos synchronization of a chaotic system via nonlinear control. Chaos Solitons Fractals 25 (2005), 579-584. DOI 10.1016/j.chaos.2004.11.038 | Zbl 1092.37514
[18] Pecora, L. M., Carroll, T. L.: Synchronization in chaotic systems. Phys. Rev. Lett. 64 (1990), 821-824. DOI 10.1103/physrevlett.64.821 | MR 1038263 | Zbl 1098.37553
[19] Rosenblum, M. G., Pikovsky, A. S., Kurths, J.: Phase synchronization of chaotic oscillators. Phys. Rev. Lett. 76 (1996), 1804-1807. DOI 10.1103/physrevlett.76.1804 | Zbl 0898.70015
[20] Sasakura, K.: On the dynamic behavior of Schinasi's business cycle model. J. Macroeconom. 16 (1994), 423-444. DOI 10.1016/0164-0704(94)90015-9
[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 10.2307/1905446 | Zbl 0050.36804
[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 10.1016/j.cnsns.2008.06.027
[23] Yang, T.: Impulsive Control Theory. Springer-Verlag, Berlin 2001. DOI 10.1007/3-540-47710-1 | MR 1850661 | Zbl 0996.93003
[24] Yang, T.: Impulsive control. IEEE Trans. Automat. Control 44 (1999), 1081-1083. DOI 10.1109/9.763234 | MR 1690562 | Zbl 1335.93013
[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 10.1109/81.633887 | MR 1488197
[26] Yang, T., Yang, L. B., Yang, C. M.: Impulsive control of Lorenz system. Physica D 110 (1997), 18-24. DOI 10.1016/s0167-2789(97)00116-4 | MR 1490790 | Zbl 0925.93414
[27] Yang, T., Yang, L. B., Yang, C. M.: Impulsive synchronization of Lorenz systems. Phys. Lett. A 226 (1997), 349-354. DOI 10.1016/s0375-9601(97)00004-2
[28] Yu, H., Cai, G., Li, Y.: Dynamic analysis and control of a new hyperchaotic finance system. Nonlinear Dynam. 67 (2012), 2171-2182. DOI 10.1007/s11071-011-0137-9 | MR 2877475 | Zbl 1242.91225
[29] Ma, M., Zhang, H., Cai, J., Zhou, J.: Impulsive practical synchronization of n-dimensional nonautonomous systems. Kybernetika 49 (2013), 539-553. MR 3117913 | Zbl 1274.70039
[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 10.1016/j.amc.2013.12.085 | MR 3214985 | Zbl 1335.91123
[31] Zheng, S.: Parameter identification and adaptive impulsive synchronization of uncertain complex-variable chaotic systems. Nonlinear Dynam. 74 (2013), 957-967. DOI 10.1007/s11071-013-1015-4 | MR 3127104 | Zbl 1306.34069
[32] Zheng, J., Du, B.: Projective synchronization of hyperchaotic financial systems. Discrete Dynamics in Nature and Society 2015 (2015), 1-9. DOI 10.1155/2015/782630 | MR 3303289
Search
Partner of
