Title:
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Chaos synchronization of TSUCS unified chaotic system, a modified function projective control method (English) |
Author:
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Tirandaz, Hamed |
Language:
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English |
Journal:
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Kybernetika |
ISSN:
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0023-5954 (print) |
ISSN:
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1805-949X (online) |
Volume:
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54 |
Issue:
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4 |
Year:
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2018 |
Pages:
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829-843 |
Summary lang:
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English |
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Category:
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math |
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Summary:
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The synchronization problem of the three-scroll unified chaotic system (TSUCS) is studied in this paper. A modified function projective synchronization (MFPS) method is developed to achieve this goal. Furthermore, the only parameter of the TSUCS unified chaotic system is considered unknown and estimated with an appropriate parameter estimation law. MFPS method is investigated for both identical and non-identical chaotic systems. Lyapunov stability theorem is utilized to verify the proposed feedback control laws and validate the proposed synchronization scheme. Finally, some numerical simulations are presented to assess the effectiveness of the theoretical discussions. (English) |
Keyword:
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chaos synchronization |
Keyword:
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three-scroll unified chaotic system (TSUCS) |
Keyword:
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modified function projective synchronization (MFPS) |
Keyword:
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nonlinear dynamics |
MSC:
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65Pxx |
MSC:
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93Cxx |
MSC:
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93Dxx |
idZBL:
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Zbl 06987037 |
idMR:
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MR3863259 |
DOI:
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10.14736/kyb-2018-4-0829 |
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Date available:
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2018-10-30T14:57:15Z |
Last updated:
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2020-01-05 |
Stable URL:
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http://hdl.handle.net/10338.dmlcz/147427 |
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Reference:
|
[1] Adloo, H., Roopaei, M.: Review article on adaptive synchronization of chaotic systems with unknown parameters..Nonlinear Dynamics 65 (2011), 1-2, 141-159. MR 2812015, 10.1007/s11071-010-9880-6 |
Reference:
|
[2] Aghababa, M. P., Heydari, A.: Chaos synchronization between two different chaotic systems with uncertainties, external disturbances, unknown parameters and input nonlinearities..Appl. Math. Modelling 36 (2012), 4, 1639-1652. MR 2878135, 10.1016/j.apm.2011.09.023 |
Reference:
|
[3] Cai, L., Zhou, J.: Impulsive stabilization and synchronization of electro-mechanical gyrostat systems..Nonlinear Dynamics 70 (2012) 1, 541-549. MR 2991292, 10.1007/s11071-012-0474-3 |
Reference:
|
[4] Chen, G., Ueta, T.: Yet another chaotic attractor..Int. J. Bifurcation Chaos 9 (1999), 07, 1465-1466. Zbl 0962.37013, MR 1729683, 10.1142/s0218127499001024 |
Reference:
|
[5] Chua, L. O., Lin, G.-N.: Canonical realization of chua's circuit family..IEEE Trans. Circuits Syst. 37 (1990), 7, 885-902. MR 1061874, 10.1109/31.55064 |
Reference:
|
[6] Chun-Lai, L., Mei, Z., Feng, Z., Xuan-Bing, Y.: Projective synchronization for a fractional-order chaotic system via single sinusoidal coupling..Optik - Int. J. Light Electron Optics 127 (2016), 5, 2830-2836. 10.1016/j.ijleo.2015.11.197 |
Reference:
|
[7] Du, H., Zeng, Q., Wang, C.: Modified function projective synchronization of chaotic system..Chaos, Solitons, Fractals 42 (2009), 4, 2399-2404. Zbl 1198.93011, MR 2299092, 10.1016/j.chaos.2009.03.120 |
Reference:
|
[8] Elhadj, Z., Sprott, J. C.: The unified chaotic system describing the lorenz and chua systems..Facta Univers., Ser. Electronics and Energetics 23 (2010), 3, 345-355. 10.2298/fuee1003345e |
Reference:
|
[9] al., K.-S. Hong et: Adaptive synchronization of two coupled chaotic hindmarsh-rose neurons by controlling the membrane potential of a slave neuron..Appl. Math. Modelling 37 (2013), 4, 2460-2468. MR 3002332, 10.1016/j.apm.2012.06.003 |
Reference:
|
[10] Hou, Y.-Y., Liau, B.-Y., Chen, H.-C.: Synchronization of unified chaotic systems using sliding mode controller..Math. Problems Engrg. 2012. MR 3007783 |
Reference:
|
[11] Hu, C., Jiang, H.: Stabilization and synchronization of unified chaotic system via impulsive control..In: Abstract and Applied Analysis, Hindawi Publishing Corporation 2014, pp. 1-8. MR 3228069, 10.1155/2014/369842 |
Reference:
|
[12] Li, G.-H.: Modified projective synchronization of chaotic system..Chaos, Solitons, Fractals 32 (2007), 5, 1786-1790. Zbl 1134.37331, MR 2299092, 10.1016/j.chaos.2005.12.009 |
Reference:
|
[13] Li, C., Liao, X., Zhang, X.: Impulsive synchronization of chaotic systems..Chaos: An Interdisciplinary J. Nonlinear Sci. 15 (2005), 2, 023104. MR 2150221, 10.1063/1.1899823 |
Reference:
|
[14] Liang, H., Wang, Z., Yue, Z., Lu, R.: Generalized synchronization and control for incommensurate fractional unified chaotic system and applications in secure communication..Kybernetika 48 (2012), 2, 190-205. Zbl 1256.93084, MR 2954320 |
Reference:
|
[15] Lorenz, E. N.: Deterministic nonperiodic flow..J. Atmospher. Sci. 20 (1963), 2, 130-141. 10.1175/1520-0469(1963)020<0130:dnf>2.0.co;2 |
Reference:
|
[16] Lü, J., Chen, G.: A new chaotic attractor coined..Int. J. Bifurcation Chaos 12 (2002), 03, 659-661. Zbl 1063.34510, MR 1894886, 10.1142/s0218127402004620 |
Reference:
|
[17] Lü, J., Chen, G., Cheng, D., Čelikovský, S.: Bridge the gap between the Lorenz system and the Chen system..Int. J. Bifurcation Chaos 12 (2002), 12, 2917-2926. MR 1956411, 10.1142/s021812740200631x |
Reference:
|
[18] Ma, T., Zhang, J., Zhou, Y., Wang, H.: Adaptive hybrid projective synchronization of two coupled fractional-order complex networks with different sizes..Neurocomputing 164 (2015), 182-189. 10.1016/j.neucom.2015.02.071 |
Reference:
|
[19] Mainieri, R., Rehacek, J.: Projective synchronization in three-dimensional chaotic systems..Phys. Rev. Lett. 82 (1999), 15, 3042. 10.1103/physrevlett.82.3042 |
Reference:
|
[20] Nik, H. S., Saberi-Nadjafi, J., Effati, S., Gorder, R. A. Van: Hybrid projective synchronization and control of the baier-sahle hyperchaotic flow in arbitrary dimensions with unknown parameters..Appl. Math. Comput. 248 (2014), 55-69. MR 3276664, 10.1016/j.amc.2014.08.108 |
Reference:
|
[21] Ott, E., Grebogi, C., Yorke, J. A.: Controlling chaos..Phys. Rev. Lett. 64 (1990), 11, 1196-1199. Zbl 0964.37502, MR 1041523, 10.1103/physrevlett.64.1196 |
Reference:
|
[22] Pan, L., Zhou, W., Fang, J., Li, D.: Synchronization and anti-synchronization of new uncertain fractional-order modified unified chaotic systems via novel active pinning control..Comm. Nonlinear Sci. Numer. Simul. 15 (2010), 12, 3754-3762. MR 2652647, 10.1016/j.cnsns.2010.01.025 |
Reference:
|
[23] Pan, L., Zhou, W., Fang, J., Li, D.: A new three-scroll unified chaotic system coined..Int. J. Nonlinear Sci. 10 (2010), 4, 462-474. MR 2834932 |
Reference:
|
[24] Park, J. H.: Adaptive synchronization of a unified chaotic system with an uncertain parameter..Int. J. Nonlinear Sci. Numer. Simulation 6 (2005), 2, 201-206. MR 3110160, 10.1515/ijnsns.2005.6.2.201 |
Reference:
|
[25] Pecora, L. M., Carroll, T. L.: Synchronization in chaotic systems..Phys. Rev. Lett. 64 (1990), 8, 821. Zbl 1098.37553, MR 1038263, 10.1103/physrevlett.64.821 |
Reference:
|
[26] Richter, H.: Controlling chaotic systems with multiple strange attractors..Physics Letters A 300 (2002), 2, 182-188. MR 1928022, 10.1016/s0375-9601(02)00183-4 |
Reference:
|
[27] Rosenblum, M. G., Pikovsky, A. S., Kurths, J.: From phase to lag synchronization in coupled chaotic oscillators..Phys. Rev. Lett. 78 (1997), 22, 4193. MR 1869044, 10.1103/physrevlett.78.4193 |
Reference:
|
[28] Shen, C., Yu, S., Lü, J., Chen, G.: A systematic methodology for constructing hyperchaotic systems with multiple positive Lyapunov exponents and circuit implementation..IEEE Tran. Circuits Systems I 61 (2014), 3, 854-864. 10.1109/tcsi.2013.2283994 |
Reference:
|
[29] Shen, C., Yu, S., Lü, J., Chen, G.: Designing hyperchaotic systems with any desired number of positive Lyapunov exponents via a simple model..IEEE Trans. Circuits Systems I 61 (2014), 8, 2380-2389. 10.1109/tcsi.2014.2304655 |
Reference:
|
[30] Sun, J., Shen, Y., Wang, X., Chen, J.: Finite-time combination-combination synchronization of four different chaotic systems with unknown parameters via sliding mode control..Nonlinear Dynamics 76 (1) (2014) 383-397. MR 3189178, 10.1007/s11071-013-1133-z |
Reference:
|
[31] Tan, S., Wang, Y., Lü, J.: Analysis and control of networked game dynamics via a microscopic deterministic approach..IEEE Trans. Automat. Control 61 (2016), 12, 4118-4124. MR 3582527, 10.1109/tac.2016.2545106 |
Reference:
|
[32] Tirandaz, H.: On adaptive modified projective synchronization of a supply chain management system..Pramana 89 (2017), 6. 10.1007/s12043-017-1482-0 |
Reference:
|
[33] Tirandaz, H., Aminabadi, S. Saiedi, Tavakoli, H.: Chaos synchronization and parameter identification of a finance chaotic system with unknown parameters, a linear feedback controller..In: Alexandria Engineering Journal, 2017. 10.1016/j.aej.2017.03.041 |
Reference:
|
[34] Wang, Q., Yu, S., Li, C., Lü, J., Fang, X., Guyeux, C., Bahi, J. M.: Theoretical Design and FPGA-based implementation of higher-dimensional digital chaotic systems..IEEE Trans. Circuits Systems I 63 (2016), 3, 401-412. MR 3488842, 10.1109/tcsi.2016.2515398 |
Reference:
|
[35] Wu, X., Guan, Z.-H., Li, T.: Chaos synchronization between unified chaotic system and genesio system..In: International Symposium on Neural Networks, Springer, 2007, pp. 8-15. 10.1007/978-3-540-72393-6\_2 |
Reference:
|
[36] Wu, X., Li, J., Upadhyay, R. K.: Chaos control and synchronization of a three species food chain model via Holling functional response..Int. J. Comput. Math. 87 (2010) 199-214. MR 2598736, 10.1080/00207160801993232 |
Reference:
|
[37] Wu, H., Xu, B. L., Fan, C., Wu, X. Y.: Chaos synchronization between unified chaotic system and Rossler system..In: Applied Mechanics and Materials 321, Trans. Tech. Publ. 2013, pp. 2464-2470. MR 2333731, 10.4028/www.scientific.net/amm.321-324.2464 |
Reference:
|
[38] Yan, Z.: Chaos Q-S synchronization between Rossler system and the new unified chaotic system..Phys. Lett. A 334 (2005), 4, 406-412. 10.1016/j.physleta.2004.11.042 |
Reference:
|
[39] Yazdanbakhsh, O., Hosseinnia, S., Askari, J.: Synchronization of unified chaotic system by sliding mode/mixed h 2/h control..Nonlinear Dynamics 67 (2012), 3, 1903-1912. MR 2877427, 10.1007/s11071-011-0117-0 |
Reference:
|
[40] Yu, Y.: Adaptive synchronization of a unified chaotic system..Chaos, Solitons, Fractals 36 (2008), 2, 329-333. 10.1016/j.chaos.2006.06.104 |
Reference:
|
[41] Yu, J., Chen, B., Yu, H., Gao, J.: Adaptive fuzzy tracking control for the chaotic permanent magnet synchronous motor drive system via backstepping..Nonlinear Analysis: Real World Appl. 12 (2011), 1, 671-681. MR 2729052, 10.1016/j.nonrwa.2010.07.009 |
Reference:
|
[42] Zhang, X., Zhu, H., Yao, H.: Analysis and adaptive synchronization for a new chaotic system..J. Dynamical Control Systems 18 (2012), 4, 467-477. MR 2980534, 10.1007/s10883-012-9155-2 |
Reference:
|
[43] Zhao, Q., Yin, H.: Gbits/s physical-layer stream ciphers based on chaotic light..Optik, Elsevier 124 (2013) 15, 2161-2164. 10.1016/j.ijleo.2012.06.075 |
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