SYNCHRONIZATION OF DIFFERENT DIMENSIONAL CHAOTIC SYSTEMS WITH TIME VARYING PARAMETERS, DISTURBANCES AND INPUT NONLINEARITIES

A. M. A. El-Sayed; A. Elsaid; H. M. Nour; A. Elsonbaty

doi:10.11948/2014017

2014 Volume 4 Issue 4

Article Contents

Article navigation > Journal of Applied Analysis & Computation > 2014 > 4(4): 323-338

Next Article Previous Article

A. M. A. El-Sayed, A. Elsaid, H. M. Nour, A. Elsonbaty. SYNCHRONIZATION OF DIFFERENT DIMENSIONAL CHAOTIC SYSTEMS WITH TIME VARYING PARAMETERS, DISTURBANCES AND INPUT NONLINEARITIES[J]. Journal of Applied Analysis & Computation, 2014, 4(4): 323-338. doi: 10.11948/2014017

Citation:

A. M. A. El-Sayed, A. Elsaid, H. M. Nour, A. Elsonbaty. SYNCHRONIZATION OF DIFFERENT DIMENSIONAL CHAOTIC SYSTEMS WITH TIME VARYING PARAMETERS, DISTURBANCES AND INPUT NONLINEARITIES[J]. Journal of Applied Analysis & Computation, 2014, 4(4): 323-338. doi: 10.11948/2014017

SYNCHRONIZATION OF DIFFERENT DIMENSIONAL CHAOTIC SYSTEMS WITH TIME VARYING PARAMETERS, DISTURBANCES AND INPUT NONLINEARITIES

1 Faculty of Science, Alexandria University, Alexandria, Egypt;
2 Mathematics and Engineering Physics Department, Faculty of Engineering, Mansoura University, PO 35516, Mansoura, Egypt

Abstract

Abstract

In this paper, the problems of robust exponential generalized and robust exponential Q-S chaos synchronization are investigated between different dimensional chaotic systems. We consider the more practical and realistic cases when unknown time varying parameters with uncertainties, environmental disturbances, and nonlinearity of input control signals are present. The adaptive technique is employed to design the appropriate controllers and the validity of the proposed controllers are proved using Lyapunov stability theorem. Furthermore, numerical simulations are performed to show the efficiency of the presented scheme.
- Chaos synchronization /
- disturbances /
- time-varying parameters /
- input nonlinearity
MSC: 34C28;93C40;37N35

FullText(HTML)

References

[1]	M.P. Aghabab and A. Heydari, Chaos synchronization between two different chaotic systems with uncertainties, external disturbances, unknown parameters and input nonlinearities, Appl. Math. Model., 36(2012), 1639-1652. Google Scholar
[2]	S. Boccaletti, J. Kurthsc, G. Osipovd, D.L. Valladaresb and C.S. Zhouc, The synchronization of chaotic systems, Physics Reports, 366(2002), 1-101. Google Scholar
[3]	Y. Chai, L. Chen, R. Wu and J. Dai, Q-S synchronization of the fractionalorder unified system, PRAMANA-journal of physic, 80(2013), 449-461. Google Scholar
[4]	G. Chen, Controlling chaotic and hyperchaotic systems via a simple adaptive feedback controller, Computers and Mathematics with Applications, 61(2011), 2031-2034. Google Scholar
[5]	G. Chen and X. Yu, Chaos Control-Theory and Applications, Springer, 2003. Google Scholar
[6]	Z. Chen, Y. Yang, G. Qi and Z. Yuan, A novel hyperchaos system only with one equilibrium, Phys. Lett. A., 360(2007), 696-701. Google Scholar
[7]	E.M. Elabbasy, H.N. Agiza and M.M. El-Dessoky, Global synchronization criterion and adaptive synchronization for new chaotic system, Chaos, Solitons and Fractals, 23(2005), 1299-1309. Google Scholar
[8]	E.M. Elabbasy, H.N. Agiza and M.M. El-Dessoky, Adaptive synchronization of a hyperchaotic system with uncertain parameter, Chaos, Solitons and Fractals, 30(2006), 1133-1142. Google Scholar
[9]	A.M.A. El-Sayed, A. Elsaid, H.M. Nour and A. Elsonbaty, Dynamical behavior, chaos control and synchronization of a memristor-based ADVP circuit, Commun. Nonlinear Sci. Numer. Simulat., 18(2013), 148-170. Google Scholar
[10]	A.M.A. El-Sayed, H.M. Nour, A. Elsaid, A.E. Matouk and A. Elsonbaty, Circuit realization, bifurcations, chaos and hyperchaos in a new 4D system, Appl. Math. Comp., 239(2014), 333-345. Google Scholar
[11]	W.D. Feng and H. Pu, Adaptive generalized functional synchronization of chaotic systems with unknown parameters, Chin. Phys. B, 17(2008), 3603-3608. Google Scholar
[12]	G. Fu, Robust adaptive modified function projective synchronization of different hyperchaotic systems subject to external disturbance, Commun Nonlinear Sci Numer Simulat., 17(2012), 2602-2608. Google Scholar
[13]	G. Gambino, M.C. Lombardo and M. Sammartino, Global linear feedback control for the generalized Lorenz system, Chaos, Solitons and Fractals, 29(2006), 829-837. Google Scholar
[14]	Z. Gang, L. Zeng-rong and M.A. Zhong-jun, Generalized synchronization of continuous dynamical system, Appl. Math. Mech. (English Edition), 28(2007), 157-162. Google Scholar
[15]	T. Gao and Z. Chen, A new image encryption algorithm based on hyper-chaos, Physics Letters A, 372(2008), 394-400. Google Scholar
[16]	A.S. Hegazi, E. Ahmed and A.E. Matouk, On chaos control and synchronization of the commensurate fractional order Liu system, Commun Nonlinear Sci Numer Simulat, 18(2013), 1193-1202. Google Scholar
[17]	M. Hu and Z. Xu, A general scheme for Q-S synchronization of chaotic systems, Nonlin. Anal., 69(2008), 1091-1099. Google Scholar
[18]	E.M. Izhikevich, Dynamical Systems in Neuroscience:The Geometry of Excitability and Bursting, Mit Press, 2007. Google Scholar
[19]	W. Jawaad, M.S.M. Noorani and M.M. Al-sawalha, Anti-Synchronization of chaotic systems via adaptive sliding mode control, Chin. Phys. Lett., 29(2012), 1-3. Google Scholar
[20]	W. Jawaad, M.S.M. Noorani and M.M. Al-sawalha, Robust active sliding mode anti-synchronization of hyperchaotic systems with uncertainties and external disturbances, Nonlin. Anal. Real World Applications, 13(2012), 2403-2413. Google Scholar
[21]	H.R. Karimi, M. Zapateiro and N. Luo, Adaptive synchronization of masterslave systems with mixed neutral and discrete time-delays and nonlinear perturbations, Asian Journal of Control, 14(2012), 251-257. Google Scholar
[22]	H.R. Karimi, Robust delay-dependent H-infinity control of uncertain time-delay systems with mixed neutral, discrete and distributed time-delays and Markovian switching parameters, IEEE Trans. Circuits and Systems I, 58(2011), 1910-1923. Google Scholar
[23]	H.R. Karimi, New delay-dependent xxponential H(infinity) synchronization for uncertain neural networks With mixed time delays, IEEE Trans. on Systems, Man and Cybernetics Part B, 40(2010), 173-185. Google Scholar
[24]	L. Kocarev and S. Lian, Chaos-Based Cryptography, Springer, 2011. Google Scholar
[25]	W.L. Li and K.M. Chang, Robust synchronization of drive-response chaotic systems via adaptive sliding mode control, Chaos, Solitons and Fractals, 39(2009), 2086-2092. Google Scholar
[26]	Z. Li and S. Shi, Robust adaptive synchronization of Rossler and Chen chaotic systems via slide technique, Phys. Lett. A, 311(2003), 389-395. Google Scholar
[27]	R.hung. Li, Exponential generalized synchronization of uncertain coupled chaotic systems by adaptive control, Commun Nonlinear Sci Numer Simulat, 14(2009), 2757-2764. Google Scholar
[28]	C. Long, S.Y. Dong and W.D. Shi, Adaptive generalized synchronization between Chen system and a multi-scroll chaotic system, Chin. Phys. B., 19(2010), 1-3. Google Scholar
[29]	A.E. Matouk, Dynamical analysis, feedback control and synchronization of Liu dynamical system, Nonlinear Analysis, 69(2008), 3213-3224. Google Scholar
[30]	A.E. Matouk and H.N. Agiza, Bifurcations, chaos and synchronization in ADVP circuit with parallel resistor, J. Math. Anal. Appl., 341(2008), 259-269. Google Scholar
[31]	E. Padmanaban, R. Banerjee and S.K. Dana, Targeting and control of synchronization in chaotic oscillators, International Journal of Bifurcation and Chaos, 22(2012), 1-12. Google Scholar
[32]	M. Pourmahmood, S. Khanmohammadi and G. Alizadeh, Synchronization of two different uncertain chaotic systems with unknown parameters using a robust adaptive sliding mode controller, Commun Nonlinear Sci Numer Simulat, 16(2011), 2853-2868. Google Scholar
[33]	N. Smaoui, A. Karouma and M. Zribi, A Secure communications based on the synchronization of the hyperchaotic Chen and the unified chaotic systems, Commun Nonlinear Sci Numer Simulat, 16(2011), 3279-3293. Google Scholar
[34]	P. Stavroulakis, Chaos Applications in Telecommunications, CRC Press, 2006. Google Scholar
[35]	Z. Sun, Function projective synchronization of two four-scroll hyperchaotic systems with unknown parameters, Cent. Eur. J. Phys., 11(2013), 89-95. Google Scholar
[36]	P.N.V. Tu, Dynamical Systems-An Introduction with Applications in Economics and Biology, Springer-Verlag, 1995. Google Scholar
[37]	B. Wang, P. Shi, H.R. Karimi, Y. Songf and J. Wanga, Robust H-infinity synchronization of a hyper-chaotic system with disturbance input, Nonlinear Analysis:Real World Applications, 14(2013), 1487-1495. Google Scholar
[38]	Z.L. Wang and X.R. Shi, Adaptive Q-S synchronization of non-identical chaotic systems with unknown parameters, Nonlin. Dyn., 59(2010), 559-567. Google Scholar
[39]	J.J. Yan, M.L. Hung, T.Y. Chiang and Y.S. Yang, Robust synchronization of chaotic systems via adaptive sliding mode control, Phys. Lett. A., 356(2006), 220-225. Google Scholar
[40]	Y. Yang and Y. Chen, The generalized Q-S synchronization between the generalized Lorenz canonical form and the Rossler system, Chaos, Solitons and Fractals, 39(2009), 2378-2385. Google Scholar
[41]	G. Zhang, Z. Liu and Z. Ma, Generalized synchronization of different dimensional chaotic dynamical systems, Chaos, Solitons and Fractals, 32(2007), 773-779. Google Scholar
[42]	C. Zhu, A novel image encryption scheme based on improved hyperchaotic sequences, Opt. Commun., 285(2012), 29-37. Google Scholar