Synchronization of fractional-order LU system with new parameters using the feedback control technique
Subject Areas : Dynamical systems and ergodic theory
1 - Department of Mathematics, Payame Noor University, Iran
2 - Department of Mathematics, Payame Noor University, Iran
Keywords:
Abstract :
[1] W. M. Ahmad, Hyperchaos in fractional order nonlinear systems, Chaos. Solitons & Fractals. 27 (2005), 1459-1465.
[2] B. Bandyopadhyay, S. Kamal, Stabilization and Control of Fractional Order Systems: A Sliding Mode Approach, Springer, 2015.
[3] N. A. Camacho, D. Mermoud, J. A. Gallegos, Lyapunov functions for fractional order system, Common. Nonlinear. Sci. Numer. Simulate. 19 (2014), 2951-2957.
[4] L. P. Chen, Y. Chai, R. W. Wu, J. Sun, T. D. Ma, Cluster synchronization in fractional-order complex dynamical networks, Phys. Lett. A. 376 (2012), 2381-2388.
[5] J. Chen, H. Liu, J. Lu, Q. Zhang, Projective and lag synchronization of a novel hyperchaotic system via impulsive control, Commun. Nonlinear. Sci. Numer. Simulat. 16 (2011), 2033-2040.
[6] W. H. Deng, C. P. Li, Chaos synchronization of the fractional Lu system, Physica A. 353 (2005), 61-72.
[7] Y. Gao, CH. Liang, Q. Wu, H. Yuan, A new fractional-order hyperchaotic system and its modified projective synchronization. Chaos. Solitons & Fractals. 76 (2015), 190-204.
[8] Z. M. Ge, C. Y. Qu, Chaos in a fractional order modified Duffing system, Chaos. Solitons & Fractals. 34 (2007), 262-291.
[9] D. Ghosh, S. Bhattacharya, Projective synchronization of new hyperchaotic system with fully unknown parameters, Nonlinear Dyn. 61 (2010), 11-21.
[10] T. T. Hartley, C. F. Lorenzo, Dynamics and control of initialzed fractional-order systems, Nonlinear Dyn. 29 (2002), 201-233.
[11] O. Heaviside, Electromagnetic Theory, Chelsea, New York, 1971.
[12] A. S. Hegazi, E. Ahmed, A. E. Matouk, On chaos control and synchronization of the commensurate fractional order Liu system, Commun. Nonlinear. Sci. Numer. Simulat. 18 (2013), 1193-1202.
[13] R. Hifer, Applications of Fractional Calculus in Physics, Word scientific, Hackensack, 2001.
[14] X. Huang, Z. Zhao, Z. Wang, Y. X. Li, Chaos and hyperchaos in fractional-order cellular neural networks, Neurocomputing. 94 (2012), 13-21.
[15] M. Ichise, Y. Nagayangi, T. Kojima, An analog simulation of noninteger order transfer functions for analysis of electrode process, J. Electroanal. Chem. 33 (1971), 253-265.
[16] R. C. Koeller, Application of fractional calculus to the theory of viscoelasticity, J. Appl. Mech. 51 (1984), 299-307.
[17] D. Kunsezov, A. Bulages, G. D. Dang, Quantum Lery processes and fractional kinetics, Phys. Rev. Lett. 82 (1999), 1136-1139.
[18] N. Laskin, Fractional marcet dynamics, Phys. A. 287 (2000), 482-492.
[19] C. Li, Tracking control and generalized projective synchronization of a class of hyperchaotic system with unknown parameter and disturbance, Commun. Nonlinear. Sci. Numer. Simulat. 17 (2012), 405-413.
[20] C. Li, W. Deng, Remarks on fractional derivatives, Appl. Math. Comput. 187 (2007), 777-784.
[21] H-L. Li, Y-L. Jiang, Z-L. Wang, Anti-synchronization and intermittent anti-synchronization of two identical hyperchaotic Chua systems via impulsive control, Nonlinear Dyn. 79 (2015), 919-925.
[22] H. Q. Li, X. F. Liao, M. W. Lou, A novel non-equilibrium fractional-order chaotic system and its complete synchronization by circuit implementation, Nonlinear Dyn. 68 (2012), 137-149.
[23] L. Liu, D. Liang, Ch. Liu, Nonlinear state-observer control for projective synchronization of a fractional-order hyperchaotic system, Nonlinear Dyn. 69 (2012), 1929-1939.
[24] J. G. Lu, Chaotic dynamics of the fractional-order Lü system and its synchronization, Physics Lett. A. 354 (2006), 305-311.
[25] D. Matignon, Stability results for fractional differential equations with applications to control processing, Comput. Engin. Systems. Appl. 2 (1996), 963-968.
[26] I. Petras, Fractional-Order Nonlinear Systems Modeling, Analysis and Aimulation, Springer, Heidelberg, 2011.
[27] I. Podlubny, Fractionaln Differential Equations, Academic press, New York, 1999.
[28] M. Rafikov, J. M. Balthazar, On control and synchroni zation in chaotic and hyperchao tic systems via linear feedback control, Commun. Nonlinear. Sci. Numer. Simulat. 13 (2008), 1246-1255.
[29] D. Sadaoui, A. Boukabou, S. Hadef, Predictive feedback control and synchronization of hyperchaotic systems, Appl. Math. Comput. 247 (2014), 235-243.
[30] S. Singh, Single input sliding mode control for hyperchaotic Lu system with parameter uncertainty, Int. J. Dynam. Control. 4 (2016), 504-514.
[31] K. S. Sudheer, M. Sabir, Adaptive modified function projective synchronization between hyperchaotic Lorenz system and hyperchaotic Lu system with uncertain parameters, Physics Lett. A. 373 (2009), 3743-3748.
[32] H. H. Sun, A. Abdelwahed, B. Onaral, Linear approximation for transfer function with a pole of fractional-order, Trans. Autom. Control. 29 (1984), 441-444.
[33] Z-L. Wang, Projective synchronization of hyperchaotic Lü system and Liu system, Nonlinear Dyn. 59 (2010), 455-462.
[34] H. Wang, Z. Z. Han, Z. Mo, Synchronization of hyperchaotic systems via linear control, Commun. Nonlinear. Sci. Numer. Simulat. 15 (2010), 1910-1920.
[35] H. Wang, H. Zhengzhi, Chaotic synchronization and secure communication based on descriptor observer, Nonlinear Dyn. 57 (2009), 69-73.
[36] Ch. Yang, Adaptive synchronization of Lü hyperchaotic system with uncertain parameters based on single-input controller, Nonlinear Dyn. 63 (2011), 447-454.
[37] C. Yin, S. Dadras, S. M. Zhang, Y. Q. Chen, Control of a novel class of fractional-order chaotic systems via adaptive sliding mode control approach, Appl. Math. Model. 37 (2013), 2469-2483.
[38] Y. Yu, H-X. Li, Adaptive generalized function projective synchronization of uncertain chaotic systems, Nonlinear Anal. 11 (2010), 2456-2464.
[39] W-X. Yuan, F. Bing, Generalized projective synchronization of a class of hyperchaotic systems based on state observer, Commun. Nonlinear. Sci. Numer. Simulat. 17 (2012), 953-963.
[40] Q. Zhang, J. Xiao, X-Q. Zhang, D-Y. Cao, Dual projective synchronization between integer-order and fractional-order chaotic systems, Optik. 141 (2017), 90-98.
[41] R. Z. Zhang, S. P. Yang, Stabilization of fractional-order chaotic system via a single state adaptive feedback controller, Nonlinear Dyn. 68 (2012), 45-51.
[42] X. Zhou, Y. Wu, Y. Li, H. Xue, Adaptive control and synchronization of a new modified hyperchaotic Lu system with uncertain parameters, Chaos. Solitons & Fractals. 39 (2009), 2477-2483.