Modified function projective synchronization between two fractional-order complex dynamical networks with unknown parameters and unknown bounded external disturbances. (English) Zbl 07566441
Summary: This paper investigates the problem of modified function projective synchronization between two fractional-order complex dynamical networks with unknown parameters and unknown bounded external disturbances. Based on the stability theory of fractional-order differential system, a new robust adaptive control scheme is designed to achieve modified function projective synchronization for two fractional-order complex dynamical networks, which is able to estimate all unknown parameters and attenuate all random uncertainties of the fractional-order complex dynamical networks. Moreover, there is no need to know the norm-bounds of all random uncertainties, and the compensator gains can be automatically adapted to suitable constants. Numerical examples are provided to show the effectiveness of proposed methods.
MSC:
| 82-XX | Statistical mechanics, structure of matter |
Keywords:
modified function projective synchronization; fractional-order; complex dynamical network; unknown parameter; external disturbanceReferences:
| [1] | Lü, J.; Yu, X.; Chen, G., Chaos synchronization of general complex dynamical networks, Physica A, 334, 281-302 (2004) |
| [2] | Zhao, M.; Zhang, H. G.; Wang, Z. L.; Liang, H. J., Observer-based lag synchronization between two different complex networks, Commun. Nonlinear Sci. Numer. Simul., 19, 2048-2059 (2014) · Zbl 1457.93053 |
| [3] | Li, X., Phase synchronization in complex networks with decayed long-range interactions, Physica D, 223, 242-247 (2006) · Zbl 1112.34028 |
| [4] | Wang, M.; Wang, X.; Niu, Y., Projective synchronization of a complex network with different fractional order chaos nodes, China Phys. B, 20, Article 010508 pp. (2011) |
| [5] | Chen, Y.; Li, X., Function projective synchronization between two identical chaotic systems, Internat. J. Modern Phys. C, 18, 883-888 (2007) · Zbl 1139.37301 |
| [6] | Du, H.; Zeng, Q.; Wang, C.; Ling, M., Function projective synchronization in coupled chaotic systems, Nonlinear Anal. RWA, 11, 705-712 (2010) · Zbl 1181.37039 |
| [7] | Wu, X.; Wang, H.; Lu, H., Hyperchaotic secure communication via generalized function projective synchronization, Nonlinear Anal. RWA, 12, 1288-1299 (2011) · Zbl 1203.94128 |
| [8] | Du, H.; Zeng, Q.; Wang, C., Modified function projective synchronization of chaotic system, Chaos Solitons Fractals, 42, 2399-2404 (2009) · Zbl 1198.93011 |
| [9] | Zhou, P.; Zhu, W., Function projective synchronization for fractional-order chaotic systems, Nonlinear Anal. RWA, 12, 811-816 (2011) · Zbl 1209.34065 |
| [10] | Sebastian Sudheer, K.; Sabir, M., Function projective synchronization in chaotic and hyperchaotic systems through open-plus-closed-loop coupling, Chaos, 20, Article 013115 pp. (2010) · Zbl 1311.34100 |
| [11] | Mahmoud, G. M.; Ahmed, M. E.; Abed-Elhameed, T. M., On fractional-order hyperchaotic complex systems and their generalized function projective combination synchronization, Optik, 130, 398-406 (2017) |
| [12] | Zhang, R.; Yang, Y.; Xu, Z.; Hu, M., Function projective synchronization in drive-response dynamical network, Phys. Lett. A, 374, 3025-3028 (2010) · Zbl 1237.34034 |
| [13] | Du, H., Function projective synchronization in drive-response dynamical networks with non-identical nodes, Chaos Solitons Fractals, 44, 510-514 (2011) · Zbl 1223.93041 |
| [14] | Du, H.; Shi, P.; Lü, N., Function projective synchronization in complex dynamical networks with time delay via hybrid feedback control, Nonlinear Anal. RWA, 14, 1182-1190 (2013) · Zbl 1258.93060 |
| [15] | Lü, L.; Li, C.; Chen, L., Outer synchronization between uncertain networks with adaptive scaling function and different node numbers, Physica A, 506, 909-918 (2018) · Zbl 1514.93013 |
| [16] | Du, H., Adaptive open-plus-closed-loop control method of modified function projective synchronization in complex networks, Int. J. Mod. Phys. C, 22, 1393-1407 (2011) · Zbl 1260.93006 |
| [17] | Hartley, T.; Lorenzo, C.; Qammer, H., Chaos in a fractional order Chua’s system, IEEE Trans. Circuits Syst. I, 42, 485-490 (1995) |
| [18] | Grigorenko, I.; Grigorenko, E., Chaotic dynamics of the fractional Lorenz system, Phys. Rev. Lett., 91, Article 034101 pp. (2003) |
| [19] | Li, C.; Chen, G., Chaos in the fractional order Chen system and its control, Chaos Solitons Fractals, 22, 549-554 (2004) · Zbl 1069.37025 |
| [20] | Gallegos, J. A.; Duarte-Mermoud, M. A., On the Lyapunov theory for fractional order systems, Appl. Math. Comput., 287-288, 161-170 (2016) · Zbl 1410.34017 |
| [21] | Aguila-Camacho, N.; Duarte-Mermoud, M. A., Boundedness of the solutions for certain classes of fractional differential equations with application to adaptive systems, ISA Trans., 60, 82-88 (2016) |
| [22] | Kengne, R.; Tchitnga, R.; Mabekou, S., On the relay coupling of three fractional-order oscillators with time-delay consideration: Global and cluster synchronizations, Chaos Solitons Fractals, 111, 6-17 (2018) · Zbl 1392.34091 |
| [23] | Mahmoud, G. M.; Abed-Elhameed, T. M.; Ahmed, M. E., Generalization of combination-combination synchronization of chaotic n-dimensional fractional-order dynamical systems, Nonlinear Dynam., 83, 1885-1893 (2016) · Zbl 1353.34060 |
| [24] | Mahmoud, G. M.; Arafa, A. A.; Abed-Elhameed, T. M.; Mahmoud, E. E., Chaos control of integer and fractional orders of chaotic Burke-Shaw system using time delayed feedback control, Chaos Solitons Fractals, 104, 680-692 (2017) · Zbl 1380.93120 |
| [25] | Mahmoud, G. M.; Ahmed, M. E.; Abed-Elhameed, T. M., Active control technique of fractional-order chaotic complex systems, Eur. Phys. J. Plus, 131, 1-11 (2016) |
| [26] | Kengne, R.; Tchitnga, R.; Tchikankou, A. N.; Kouanou, A. T.; Fomethe, A., Dynamical properties and finite-time hybrid projective synchronization using fractional nonsingular sliding mode surface in fractional-order two-stage colpitts oscillators, J. Chaos, 2013, Article 839038 pp. (2013) |
| [27] | Kengne, R.; Tchitnga, R.; Fomethe, A.; Hammouch, Z., Generalized finite-time function projective synchronization of two fractional-order chaotic systems via a modified fractional nonsingular sliding mode surface, Commun. Numer. Anal., 2, 233-248 (2017) |
| [28] | Velmurugana, G.; Rakkiyappan, R.; Vembarasanb, V.; Cao, J.; Alsaedi, A., Dissipativity and stability analysis of fractional-order complex-valued neural networks with time delay, Neural Netw., 86, 42-53 (2017) · Zbl 1432.34101 |
| [29] | Wang, Y.; Li, T., Synchronization of fractional order complex dynamical networks, Physica A, 428, 1-12 (2015) · Zbl 1400.34088 |
| [30] | Fang, Q.; Peng, J., Synchronization of fractional-order linear complex networks with directed coupling topology, Physica A, 490, 542-553 (2018) · Zbl 1514.34085 |
| [31] | Wonga, W.; Li, H.; Leung, S., Robust synchronization of fractional-order complex dynamical networks with parametric uncertainties, Commun. Nonlinear Sci. Numer. Simul., 17, 4877-4890 (2012) · Zbl 1261.93008 |
| [32] | Liang, S.; Wu, R.; Chen, L., Adaptive pinning synchronization in fractional-order uncertain complex dynamical networks with delay, Physica A, 444, 49-62 (2016) · Zbl 1400.93142 |
| [33] | Bao, H.; Park, J. H.; Cao, J., Adaptive synchronization of fractional-order memristor-based neural networks with time delay, Nonlinear Dynam., 82 (2015), 1343-54 · Zbl 1348.93159 |
| [34] | Yang, Y.; Wang, Y.; Li, T., Outer synchronization of fractional-order complex dynamical networks, Optik, 127, 7395-7407 (2016) |
| [35] | Bao, H.; Park, J. H.; Cao, J., Synchronization of fractional-order complex-valued neural networks with time delay, Neural Netw., 81, 16-28 (2016) · Zbl 1417.34190 |
| [36] | Velmurugan, G.; Rakkiyappan, R.; Cao, J., Finite-time synchronization of fractional-order memristor-based neural networks with time delays, Neural Netw., 73, 36-46 (2016) · Zbl 1398.34110 |
| [37] | Duarte-Mermoud, M. A.; Aguila-Camacho, N.; Gallegos, J. A.; Castro-Linares, R., Using general quadratic Lyapunov functions to prove Lyapunov uniform stability for fractional order systems, Commun. Nonlinear Sci. Numer. Simul., 22, 650-659 (2015) · Zbl 1333.34007 |
| [38] | Li, Y.; Chen, Y.; Podlubny, I., Mittag-Leffler stability of fractional order nonlinear dynamic systems, Automatica, 45, 1965-1969 (2009) · Zbl 1185.93062 |
| [39] | Kengne, R.; Tchitnga, R.; Mezatio, A.; Fomethe, A.; Litak, G., Finite-time synchronization of fractional-order simplest two-component chaotic oscillators, Eur. Phys. J. B, 90, 88 (2017) |
| [40] | Giresse, T. A.; Crépin, K. T., Chaos generalized synchronization of coupled Mathieu-Van der Pol and coupled Duffing-Van der Pol systems using fractional order-derivative, Chaos Solitons Fractals, 98, 88-100 (2017) · Zbl 1372.34114 |
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