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Finite-time multi-switching synchronization behavior for multiple chaotic systems with network transmission mode. (English) Zbl 1393.93057
Summary: By considering network transmission mode, this paper addresses the finite-time multi-switching synchronization problem for two kinds of multiple chaotic systems. For multiple same-order chaotic systems, we construct the general switching rules and analyze the existence of switching cases. The presented schemes guarantee the states of each derive system to be finite-timely synchronized with the desired states of every respond system in the different transmission paths and switching sequences. For multiple different order chaotic systems, we analyze a special multi-switching hybrid synchronization behavior, where part of the states are completely synchronized and the others belong to combination synchronization. Moveover, the easily verifiable criterion is derived for such synchronization. Finally, numerical examples are given to show the effectiveness of the presented theoretical results.

93C15 Control/observation systems governed by ordinary differential equations
34H10 Chaos control for problems involving ordinary differential equations
93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
Full Text: DOI
[1] Grassi, G., Propagation of projective synchronization in a series connection of chaotic systems, J. Frankl. Inst., 347, 2, 438-451, (2010) · Zbl 1185.93075
[2] Tang, Y.; Fang, J., Synchronization of n-coupled fractional-order chaotic systems with ring connection, Commun. Nonlinear Sci. Numer. Simul., 15, 2, 401-412, (2010) · Zbl 1221.34103
[3] Chen, X.; Wang, C.; Qiu, J., Synchronization and anti-synchronization of n different coupled chaotic systems with ring connection, Int. J. Modern Phys. C, 25, 5, (2014), art. no. 1440011 (12 pages)
[4] Chen, X.; Qiu, J.; Cao, J.; He, H., Hybrid synchronization behavior in an array of coupled chaotic systems with ring connection, Neurocomputing, 173, 1299-1309, (2016)
[5] Sun, J.; Cui, G.; Wang, Y.; Shen, Y., Combination complex synchronization of three chaotic complex systems, Nonlinear Dyn., 79, 2, 953-965, (2015) · Zbl 1345.34101
[6] Luo, R.; Wang, Y.; Deng, S., Combination synchronization of three classic chaotic systems using active backstepping design, Chaos, 21, 043114, (2011) · Zbl 1317.93114
[7] Sun, J.; Shen, Y.; Zhang, G. D., Transmission projective synchronization of multi-systems with non-delayed and delayed coupling via impulsive control, Chaos, 22, 043107, (2012) · Zbl 1319.34108
[8] Chen, X.; Park, J. H.; Cao, J.; Qiu, J., Sliding mode synchronization of multiple chaotic systems with uncertainties and disturbances, Appl. Math. Comput., 308, 161-173, (2017) · Zbl 1411.34087
[9] Chen, X.; Cao, J.; Qiu, J.; Alsaedi, A.; Alsaadi, F. E., Adaptive control of multiple chaotic systems with unknown parameters in two different synchronization modes, Adv. Differ. Equ., 2016, (2016), art. no. 231 · Zbl 1419.93028
[10] Chen, X.; Park, J. H.; Cao, J.; Qiu, J., Adaptive synchronization of multiple uncertain coupled chaotic systems via sliding mode control, Neurocomputing, (2017)
[11] Ucar, A.; Lonngren, K. E.; Bai, E. W., Multi-switching synchronization of chaotic systems with active controllers, Chaos Soliton Fract., 38, 254-262, (2008)
[12] Wang, X.; Sun, P., Multi-switching synchronization of chaotic system with adaptive controllers and unknown parameters, Nonlinear Dyn., 63, 4, 599-609, (2011)
[13] Ajayi, A. A.; Ojo, K. S.; Vincent, U. E.; Njah, A. N., Multi-switching synchronization of a driven hyperchaotic circuit using active backstepping, J. Nonlinear Dyn., 2014, (2014), art. no. 918586 · Zbl 1407.94194
[14] Feng, Y.; Pu, J.; Wei, Z., Switched generalized function projective synchronization of two hyperchaotic systems with hidden attractors, Eur. Phys. J. Spec. Top., 224, 1593-1604, (2015)
[15] Zhou, X.; Xiong, L.; Cai, X., Adaptive switched generalized function projective synchronization between two hyperchaotic systems with unknown parameters, Entropy, 16, 377-388, (2014) · Zbl 1338.34115
[16] Ayub, K.; Dinesh, K.; Nitish, P., Reduced order multi switching hybrid synchronization of chaotic systems, J. Math. Comput. Sci., 7, 414-429, (2017)
[17] Vincent, U. E.; Saseyi, A. O.; McClintock, P. V.E., Multi-switching combination synchronization of chaotic systems, Nonlinear Dyn., 80, 845-854, (2015) · Zbl 1345.93082
[18] Zheng, S., Multi-switching combination synchronization of three different chaotic systems via nonlinear control, Optik, 127, 10247-10258, (2016)
[19] Bhat, S. P.; Bernstein, D. S., Finite-time stability of continuous autonomous systems, SIAM J. Control Optim., 38, 3, 751-766, (2000) · Zbl 0945.34039
[20] Tang, Y.; Qian, F.; Gao, H.; Kurths, J., Synchronization in complex networks and its application: A survey of recent advances and challenges, Annu. Rev. Control, 38, 2, 184-198, (2014)
[21] Mei, J.; Jiang, M.; Xu, W.; Wang, B., Finite-time synchronization control of complex dynamical networks with time delay, Commun. Nonlinear Sci. Numer. Simul., 18, 9, 2462-2478, (2013) · Zbl 1311.34157
[22] Mei, J.; Jiang, M.; Wang, X.; Han, J., Finite-time synchronization of drive-response systems via periodically intermittent adaptive control, J. Frankl. I., 351, 5, 2691-2710, (2014) · Zbl 1372.93024
[23] Fan, Y.; Liu, H.; Zhu, Y.; Mei, J., Fast synchronization of complex dynamical networks with time-varying delay via periodically intermittent control, Neurocomputing, 205, 182-194, (2016)
[24] Yang, X.; Song, Q.; Liu, Y., Z, zhao, finite-time stability analysis of fractional-order neural networks with delay, Neurocomputing, 152, 19-26, (2015)
[25] Liu, M.; Jiang, H.; Hu, C., Finite-time synchronization of delayed dynamical networks via aperiodically intermittent control, J. Frankl. I., (2017) · Zbl 1395.93348
[26] Liu, X.; Cao, J.; Xie, C., Finite-time and fixed-time bipartite consensus of multi-agent systems under a unified discontinuous control protocol, J. Frankl. I., (2017)
[27] Cai, N.; Li, W.; Jing, Y., Finite-time generalized synchronization of chaotic systems with different order, Nonlinear Dyn., 64, 385-393, (2011)
[28] Ahmad, I.; Shafiq, M.; Saaban, A. B.; Ibrahim, A. B.; Shahzad, M., Robust finite-time global synchronization of chaotic systems with different orders, Optik, 127, 19, 8172-8185, (2016)
[29] Sun, J.; Wang, Y.; Wang, Y.; Shen, Y., Finite-time synchronization between two complex-variable chaotic systems with unknown parameters via nonsingular terminal sliding mode control, Nonlinear Dyn., 85, 2, 1105-1117, (2016) · Zbl 1355.34097
[30] Sun, J.; Wu, Y.; Cui, G.; Wang, Y., Finite-time real combination synchronization of three complex-variable chaotic systems with unknown parameters via sliding mode control, Nonlinear Dyn., (2017) · Zbl 1380.34097
[31] 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 Dyn., 76, 1, 383-397, (2013) · Zbl 1319.37027
[32] Chen, X.; Cao, J.; Park, J. H.; Qiu, J., Finite-time control of multiple different-order chaotic systems with two network synchronization modes, Circuits Syst. Signal Process., (2017)
[33] Zhang, D. Y.; Mei, J.; Mi, P., Global finite-time synchronization of different dimensional chaotic systems, Appl. Math. Model., 48, 303-315, (2017)
[34] Lü, J.; Chen, G., A new chaotic attractor coined, Int. J. Bifurc. Chaos, 12, 3, 659-661, (2002) · Zbl 1063.34510
[35] Fowler, A. C.; McGuinnes, M. J.; Gibbon, J. D., The complex Lorenz equations, Phys. D., 4, 139-163, (1982) · Zbl 1194.37039
[36] Mahmoud, E.; Mahmoud, G., On some chaotic complex nonlinear systems, (2010), Lambert Academic Publishing Germany · Zbl 1215.93114
[37] Rössler, O., An equation for hyperchaos, Phys. Lett. A., 71, 155-157, (1979) · Zbl 0996.37502
[38] Kovacic, I.; Brennan, M. J., The Duffing equation: nonlinear oscillators and their behaviour, (2011), John Wiley and Sons, Inc. · Zbl 1220.34002
[39] Zeng, Z.; Huang, T.; Zheng, W., Multistability of recurrent neural networks with time-varying delays and the piecewise linear activation function, IEEE Trans. Neur. Net., 21, 1371-1377, (2010)
[40] Huang, T.; Li, C.; Duan, S.; Starzyk, J., Robust exponential stability of uncertain delayed neural networks with stochastic perturbation and impulse effects, IEEE Trans. Neur. Net. Lear. Syst., 23, 866-875, (2012)
[41] Liu, J.; Liu, S. T.; Sprott, J. C., Adaptive complex modified hybrid function projective synchronization of different dimensional complex chaos with uncertain complex parameters, Nonlinear Dyn., 83, 1109-1121, (2016) · Zbl 1349.93221
[42] Wang, Y.; Xia, Y.; Shen, H.; Zhou, P., SMC design for robust stabilization of nonlinear Markovian jump singular systems, IEEE Trans. Autom. Control, (2018) · Zbl 1390.93695
[43] Xie, X.; Yue, D.; Ma, T.; Zhu, X., Further studies on control synthesis of discrete-time T-S fuzzy systems via augmented multi-indexed matrix approach, IEEE Trans. Cyber., 44, 12, 2784-2791, (2014)
[44] Tang, Y.; Gao, H.; Lu, J.; Kurths, J., Pinning distributed synchronization of stochastic dynamical networks: a mixed optimization approach, IEEE Trans. Neural Netw. Learn. Syst., 25, 10, 1804-1815, (2014)
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