Finite-time Generalized and Modified Generalized Projective Synchronization between Chaotic and Hyperchaotic Systems with External Disturbances
DOI:
https://doi.org/10.5890/DNC.2024.03.012Abstract
In this paper, two different types of synchronization between different chaotic systems with external disturbances in finite-time have been discussed. Further, chaotic and hyperchaotic systems have synchronized up to a desired transformation matrix. To numerically simulate generalized synchronization T chaotic system and a hyperchaotic system have been considered. In addition, modified generalized projective synchronization has been analyzed theoretically and numerically. Numerical results have shown through graphically and agreed with theoretical analysis.References
[1] Pecora, L.M. and Carroll, T.L. (1990), Synchronization in chaotic systems, Physical Review Letters, 64 (8), 821.
[2] Yadav, V.K., Shukla, V.K., Das, S., Leung, A.Y.T., and Srivastava M. (2018), Function projective synchronization of fractional order satellite system and its stability analysis for incommensurate case, Chinese Journal of Physics, 56, 696-707.
[3] Srivastava, M., Das, S. and Leung, A.Y.T. (2013), Hybrid phase synchronization between identical and non-identical three dimensional chaotic systems using active control method, Nonlinear Dynamics, 73, 2261-2272.
[4] Sun, J., Wang, Y., Wang, Y., Cui, G., and Shen, Y. (2016), Compound-combination synchronization of five chaotic systems via nonlinear control, Optik, 127(8), 4136-4143.
[5] Gonzalez-Miranda, J.M. (2002), Generalized synchronization in directionally coupled systems with identical individual dynamics. Physical Review E, 65, 047202.
[6] Kocarev, L. and Partlitz, U. (1996), Generalized synchronization, predictability, and equivalence of unidirectionally coupled dynamical systems, Physical Review Letters, 76, 1816.
[7] Rulkov, N.F., Sushchik, M.M., Tsimring, L.S., and Abarbanel H.D.I. (1995), Generalized Synchronization of chaos in directionally coupled chaotic systems, Physical Review E, 51, 980–994.
[8] Sun, J., Shen, Y., Yin, Q., and Xu, C. (2013), Compound synchronization of four memristor-chaotic oscillator systems and secure communication, Chaos: An Interdisciplinary Journal of Nonlinear Science, 23(1), 013140.
[9] Shukla, V.K., Vishal, K., Srivastava, M. (2022), Multi-switching Compound Synchronization of Different Chaotic Systems with External Disturbances and Parametric Uncertainties via Two Approaches. International Journal of Applied and Computational Mathematics, 8(1), 1-22.
[10] Wu, X.J., Wang, H., and Lu, H.T. (2012), Modified generalized projective synchronization of a new fractional-order hyperchaotic system and its application to secure communication, Nonlinear Analysis: Real World Applications, 13(3), 1441-1450.
[11] Yadav, V.K., Shukla, V.K., and Das, S. (2019), Difference synchronization among three chaotic systems with exponential term and its chaos control, Chaos, Solitons & Fractals, 124, 36-51.
[12] Hunt, B.R., Ott E., and Yorke, J.A. (1997), Differentiable generalized synchronization of chaos, Physical Review E, 55(4), 4029-4034.
[13] Zhang, G., Liu, Z., and Ma, Z. (2007), Generalized synchronization of different dimensional chaotic dynamical systems,Chaos, Solitons & Fractals, 32, 773-779.
[14] Zhang, D., Zhao, A., Yang, X., Sun, Y., and Xiao, J. (2019), Generalized Synchronization Between Chen System and Rucklidge System, IEEE Access, 7, 8519-8526.
[15] Yu, Y. and Li, H.X. (2009), Generalized synchronization of different dimensional chaotic systems based on parameter identification, Modern Physics Letters B, 23(22), 2593-2606.
[16] Guo, L., Nian, X., and Pan, H. (2013) Generalized Synchronization of Different Chaotic Systems Based on Nonnegative Off-Diagonal Structure, Mathematical Problems in Engineering, 1-8.
[17] Ouannas, A. and Al-sawalha, M.M. (2016), On $Lambda-phi$ generalized synchronization of chaotic dynamical systems in continuous-time, The European Physical Journal, 225, 187–196.
[18] Hao, Z., Xi, M. Kui, Yu, Y., and Dong, X.C. (2005), Generalized synchronization of hyperchaos and chaos using active backstepping design, Chinese Physics, 14(1), 86-94.
[19] Li, R.H. (2009), Exponential generalized synchronization of uncertain coupled chaotic systems by adaptive control, Communications in Nonlinear Science and Numerical Simulation, 14, 2757-2764.
[20] Khan, M.A., Pal, S.N., and Poria, S. (2012), Generalized anti-synchronization of different chaotic systems, International Journal of Applied Mechanics and Engineering, 17(1), 83-99.
[21] El-Sayed, A.M.A., Elsaid, A., Nour, H.M., and Elsonbaty, A. (2014), Synchronization of different dimensional chaotic systems with time varying parameters, disturbances and input nonlinearities, Journal of Applied Analysis and Computation, 4(4), 323-338.
[22] Wang, X., Wang, L., and Lin, D. (2012), Generalized (lag, anticipated and complete) projective synchronization in two non-identical chaotic systems with unknown parameters, International Journal of Modern Physics B, 26(16), 1-9.
[23] Huang, Y., Wang, Y.W., and Xiao, J.W. (2009), Generalized lag-synchronization of continuous chaotic system, Chaos, Solitons & Fractals, 40, 766-770.
[24] Gu, B., Shan, L., Li, J., and Wang, Z. (2008) Generalized Projected Synchronization of Wang and Chen hyperchaotic Systems, Proceedings of the 7th World Congress on Intelligent Control and Automation, 8626-8631.
[25] Cai, N., Li, W., and Jing, Y. (2011), Finite-time generalized synchronization of chaotic systems with different order, Nonlinear Dynamics, 64, 385–393.
[26] Cai, N., Jing, Y., and Zhang, S. (2009), Generalized projective synchronization of different chaotic systems based on anti-symmetric structure, Chaos, Solitons & Fractals, 42, 1190-1196.
[27] Li, R., Zhang, G., Zhu, T., Wang, X., and Dong, J. (2014), Generalized hybrid dislocated function projective synchronization of chaotic systems with time delay, Applied Mechanics and Materials, 574, 672-678.
[28] Li, S. and Tian, Y.P. (2003), Finite-time synchronization of chaotic systems, Chaos, Solitons & Fractals, 15(2), 303-310.
[29] Abdurahman, A., Jiang, H., and Teng, Z. (2015), Finite-time synchronization for memristor-based neural networks with time-varying delays, Neural Networks, 69, 20-28.
[30] Zhang, L., Zhong, J., and Lu, J. (2021), Intermittent control for finite-time synchronization of fractional-order complex networks, Neural Networks, 144, 11-20.
[31] Alattas, K.A., Mostafaee, J., Sambas, A., Alanazi, A.K., Mobayen, S., Vu, M.T., and Zhilenkov, A. (2021), Nonsingular integral-type dynamic finite-time synchronization for hyperchaotic systems, Mathematics, 10(1), 115.
[32] Cheng, Y., Du, H., He, Y., and Jia, R. (2015), Robust finite-time synchronization of coupled harmonic oscillations with external disturbance, Journal of the Franklin Institute, 352(10), 4366-4381.
[33] Ahmad, I. and Shafiq, M. (2022), Synchronization control of externally disturbed chaotic spacecraft in pre-assigned settling time, Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, 236(1), 87-106.
[34] Yadav, V.K., Agrawal, S.K., Srivastava, M., and Das, S. (2017), Phase and anti-phase synchronizations of fractional order hyperchaotic systems with uncertainties and external disturbances using nonlinear active control method, International Journal of Dynamics and Control, 5(2), 259-268.
[35] Mishra, A.K., Das, S., and Yadav, V.K. (2022), Finite-time synchronization of multi-scroll chaotic systems with sigmoid non-linearity and uncertain terms, Chinese Journal of Physics, 75, 235-245.
[36] Chao, S. and De, C.J. (2012), Modified generalized projective synchronization of incommensurate fractional-order chaotic systems, Proceedings of the 31st Chinese control conference, IEEE, 1065-1069.
[37] Liu, J., Liu, S., and Li, W. (2015), Complex modified generalized projective synchronization of fractional-order complex chaos and real chaos,Advances in Difference Equations, 274, 1-16.
[38] Zhou, X., Jiang, M., and Huang, Y. (2014), Switched modified function projective synchronization between two complex nonlinear hyperchaotic systems based on adaptive control and parameter identification, Kybernetika, 50(4), 632-642.
[39] Runzi, L., Shucheng, D. and Zhengmin, W. (2010), Modified projective synchronization of a hyperchaotic system with unknown and/or uncertain parameters, Journal of Vibration and Control, 17(7), 1099–1105.
[40] Liu, J. (2014), Complex modified hybrid projective synchronization of different dimensional fractional-order complex chaos and real hyper-chaos, Entropy, 16, 6195-6211.
[41] Liu, J., Liu, S., and Yuan, C. (2013), Modified generalized projective synchronization of fractional-order chaotic Lü systems, Advances in Difference Equations, 374, 1-13.
[42] Feng, Y., Sun, L., and Yu, X. (2004), Finite-time synchronization of chaotic systems with unmatched uncertainties. In 30th Annual Conference of IEEE Industrial Electronics Society, IECON, 3, 2911-2916.
[43] Tigan, G. and Opris, D. (2008), Analysis of a 3D chaotic system, Chaos, Solitons & Fractals, 36, 1315-1319.
[44] Dolvis, L.G., Vaidyanathan, S., Jacques, K., Sambas, A., Sukono, Mamat, M. (2019), A new 4-D hyperchaotic system with four-scroll hidden attractor, its properties and bifurcation analysis, Materials Science and Engineering, 621, 1-13.
[45] Liu, C., Liu, T., Liu L., and Liu, K. (2004), A new chaotic attractor, Chaos, Solitons & Fractals, 22, 1031-1038.
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