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Modified function projective synchronization between different dimension fractional-order chaotic systems. (English) Zbl 1253.34019
Summary: A modified function projective synchronization (MFPS) scheme for different dimension fractional-order chaotic systems is presented via fractional order derivative. The synchronization scheme, based on stability theory of nonlinear fractional-order systems, is theoretically rigorous. The numerical simulations demonstrate the validity and feasibility of the proposed method.

34A08Fractional differential equations
Full Text: DOI
[1] I. Podlubny, Fractional Differential Equations, vol. 198, Academic Press, San Diego, Calif, USA, 1999. · Zbl 1056.93542 · doi:10.1109/9.739144
[2] R. Hilfer, Applications of Fractional Calculus in Physics, World Scientific, River Edge, NJ, USA, 2001. · Zbl 1111.93302 · doi:10.1142/9789812817747
[3] I. Grigorenko and E. Grigorenko, “Chaotic dynamics of the fractional Lorenz system,” Physical Review Letters, vol. 91, no. 3, pp. 34101-034104, 2003.
[4] X. J. Wu, J. Li, and G. R. Chen, “Chaos in the fractional order unified system and its synchronization,” Journal of the Franklin Institute, vol. 345, no. 4, pp. 392-401, 2008. · Zbl 1166.34030 · doi:10.1016/j.jfranklin.2007.11.003
[5] T. T. Hartley, C. F. Lorenzo, and H. K. Qammer, “Chaos in a fractional order Chua’s system,” IEEE Transactions on Circuits and Systems I, vol. 42, no. 8, pp. 485-490, 1995.
[6] Z. M. Ge and C. Y. Ou, “Chaos in a fractional order modified Duffing system,” Chaos, Solitons & Fractals, vol. 34, no. 2, pp. 262-291, 2007. · Zbl 1132.37324 · doi:10.1016/j.chaos.2005.11.059
[7] Y. G. Yu and H. X. Li, “The synchronization of fractional-order Rössler hyperchaotic systems,” Physica A, vol. 387, no. 5-6, pp. 1393-1403, 2008.
[8] A. Freihat and S. Momani, “Adaptation of differential transform method for the numeric-analytic solution of fractional-order Rössler chaotic and hyperchaotic systems,” Abstract and Applied Analysis, Article ID 934219, 13 pages, 2012. · Zbl 1237.37058 · doi:10.1155/2012/934219
[9] N. X. Quyen, V. V. Yem, and T. M. Hoang, “A chaotic pulse-time modulation method for digital communication,” Abstract and Applied Analysis, vol. 2012, Article ID 835304, 15 pages, 2012. · Zbl 1242.94003 · doi:10.1155/2012/835304
[10] D. Y. Chen, W. L. Zhao, X. Y. Ma, and R. F. Zhang, “Control and cynchronization of chaos in RCL-Shunted Josephson Junction with noise disturbance using only one controller term,” Abstract and Applied Analysis, vol. 2012, Article ID 378457, 14 pages, 2012. · Zbl 1246.34060 · doi:10.1155/2012/378457
[11] Y. Y. Hou, “Controlling chaos in permanent magnet synchronous motor control system via fuzzy guaranteed cost controller,” Abstract and Applied Analysis, vol. 2012, Article ID 650863, 10 pages, 2012. · Zbl 1246.93065 · doi:10.1155/2012/650863
[12] R. Mainieri and J. Rehacek, “Projective synchronization in the three-dimensional chaotic systems,” Physical Review Letters, vol. 82, no. 15, pp. 3042-3045, 1999.
[13] Y. Yu and H.-X. Li, “Adaptive generalized function projective synchronization of uncertain chaotic systems,” Nonlinear Analysis, vol. 11, no. 4, pp. 2456-2464, 2010. · Zbl 1202.34095 · doi:10.1016/j.nonrwa.2009.08.002
[14] Y. Chen, H. An, and Z. Li, “The function cascade synchronization approach with uncertain parameters or not for hyperchaotic systems,” Applied Mathematics and Computation, vol. 197, no. 1, pp. 96-110, 2008. · Zbl 1136.93410 · doi:10.1016/j.amc.2007.07.036
[15] H. An and Y. Chen, “The function cascade synchronization method and applications,” Communications in Nonlinear Science and Numerical Simulation, vol. 13, no. 10, pp. 2246-2255, 2008. · Zbl 1221.93124 · doi:10.1016/j.cnsns.2007.05.029
[16] S. Wang, Y. G. Yu, and M. Diao, “Hybrid projective synchronization of chaotic fractional order systems with different dimension,” Physica A, vol. 389, no. 21, pp. 4981-4988, 2010.
[17] L. Pan, W. Zhou, L. Zhou, and K. Sun, “Chaos synchronization between two different fractional-order hyperchaotic systems,” vol. 16, no. 6, pp. 2628-2640, 2011. · Zbl 1221.37220 · doi:10.1016/j.cnsns.2010.09.016
[18] X. Y. Wang and J. M. Song, “Synchronization of the fractional order hyperchaos Lorenz systems with activation feedback control,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 8, pp. 3351-3357, 2009. · Zbl 1221.93091 · doi:10.1016/j.cnsns.2009.01.010
[19] R. Zhang and S. Yang, “Adaptive synchronization of fractional-order chaotic systems via a single driving variable,” Nonlinear Dynamics, vol. 66, no. 4, pp. 831-837, 2011. · Zbl 1242.93097 · doi:10.1007/s11071-011-0213-1
[20] R. X. Zhang and S. P. Yang, “Stabilization of fractional-order chaotic system via a single state adaptive-feedback controller,” Nonlinear Dynamic, vol. 68, no. 1-2, pp. 45-51, 2012. · Zbl 1243.93099
[21] D. Cafagna and G. Grassi, “Observer-based projective synchronization of fractional systems via a scalar signal: application to hyperchaotic Rössler systems,” Nonlinear Dynamic, vol. 68, no. 1-2, pp. 117-128, 2012. · Zbl 1243.93047
[22] M. S. Tavazoei and M. Haeri, “Chaos control via a simple fractional-order controller,” Physics Letters A, vol. 372, no. 6, pp. 798-807, 2008. · Zbl 1217.70022 · doi:10.1016/j.physleta.2007.08.040
[23] E. Ahmed, A. M. A. El-Sayed, and H. A. A. El-Saka, “Equilibrium points, stability and numerical solutions of fractional-order predator-prey and rabies models,” Journal of Mathematical Analysis and Applications, vol. 325, no. 1, pp. 542-553, 2007. · Zbl 1105.65122 · doi:10.1016/j.jmaa.2006.01.087
[24] Z. M. Odibat, “Adaptive feedback control and synchronization of non-identical chaotic fractional order systems,” Nonlinear Dynamics, vol. 60, no. 4, pp. 479-487, 2010. · Zbl 1194.93105 · doi:10.1007/s11071-009-9609-6
[25] Z. Odibat, “A note on phase synchronization in coupled chaotic fractional order systems,” Nonlinear Analysis, vol. 13, no. 2, pp. 779-789, 2012. · Zbl 1238.34121 · doi:10.1016/j.nonrwa.2011.08.016
[26] J. Lü, X. Yu, G. Chen, and D. Cheng, “Characterizing the synchronizability of small-world dynamical networks,” IEEE Transactions on Circuits and Systems I, vol. 51, no. 4, pp. 787-796, 2004. · doi:10.1109/TCSI.2004.823672
[27] J. Zhou, J.-a. Lu, and J. Lü, “Adaptive synchronization of an uncertain complex dynamical network,” IEEE Transactions on Automatic Control, vol. 51, no. 4, pp. 652-656, 2006. · doi:10.1109/TAC.2006.872760
[28] J. Lü and G. Chen, “A time-varying complex dynamical network model and its controlled synchronization criteria,” IEEE Transactions on Automatic Control, vol. 50, no. 6, pp. 841-846, 2005. · doi:10.1109/TAC.2005.849233
[29] J. Lü and G. Chen, “Generating multiscroll chaotic attractors: theories, methods and applications,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 16, no. 4, pp. 775-858, 2006. · Zbl 1097.94038 · doi:10.1142/S0218127406015179
[30] J. H. Lü, S. M. Yu, H Leung, and G. R. Cheng, “Experimental verification of multidirectional multiscroll chaotic attractors,” IEEE Transactions on Circuits and Systems I, vol. 53, no. 1, pp. 149-165, 2006.
[31] J. Lü, F. Han, X. Yu, and G. Chen, “Generating 3-D multi-scroll chaotic attractors: a hysteresis series switching method,” Automatica, vol. 40, no. 10, pp. 1677-1687, 2004. · Zbl 1162.93353 · doi:10.1016/j.automatica.2004.06.001
[32] J. Lü and G. Chen, “A new chaotic attractor coined,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 12, no. 3, pp. 659-661, 2002. · Zbl 1063.34510 · doi:10.1142/S0218127402004620