Stochastic quasi-synchronization of heterogeneous delayed impulsive dynamical networks via single impulsive control. (English) Zbl 1526.93266
Summary: This paper investigates the quasi-synchronization problem of the stochastic heterogeneous complex dynamical networks with impulsive couplings and multiple time-varying delays. It is shown that this kind of dynamical networks can achieve exponential quasi-synchronization by exerting impulsive control added on only one chosen pinning node. By employing the Lyapunov stability theory, some sufficient criteria on quasi-synchronization for this dynamical network are established, revealing the relationship between the quasi-synchronization performance and the stochastic perturbations as well as the frequency and strength of impulsive coupling. Finally, some numerical examples are used to illustrate the effectiveness of the main results.
MSC:
| 93E15 | Stochastic stability in control theory |
| 93C43 | Delay control/observation systems |
| 93C27 | Impulsive control/observation systems |
| 93B70 | Networked control |
Keywords:
stochastic quasi-synchronization; heterogeneous dynamical networks; impulsive coupling; time-varying delays; single impulsive controlReferences:
| [1] | Ali, M. S.; Narayanan, G.; Sevgen, S.; Shekher, V.; Arik, S., Global stability analysis of fractional-order fuzzy BAM neural networks with time delay and impulsive effects, Communications in Nonlinear Science and Numerical Simulation, 78, Article 104853 pp. (2019) · Zbl 1461.93420 |
| [2] | Chen, H.; Shi, P.; Lim, C., Pinning impulsive synchronization for stochastic reaction-diffusion dynamical networks with delay, Neural Networks, 106, 281-293 (2018) · Zbl 1443.93133 |
| [3] | Chen, H.; Shi, P.; Lim, C. C., Cluster synchronization for neutral stochastic delay networks via intermittent adaptive control, IEEE Transactions on Neural Networks and Learning Systems, 30, 11, 3246-3259 (2019) |
| [4] | Dong, H.; Luo, M.; Xiao, M., Almost sure synchronization for nonlinear complex stochastic networks with Lévy noise, Nonlinear Dynamics, 95, 2, 957-969 (2019) · Zbl 1439.62205 |
| [5] | Fan, J.; Wang, Z.; Jiang, G., Quasi-synchronization of heterogeneous complex networks with switching sequentially disconnected topology, Neurocomputing, 237, 342-349 (2017) |
| [6] | Gao, L.; Wang, D.; Wang, G., Further results on exponential stability for impulsive switched nonlinear time-delay systems with delayed impulse effects, Applied Mathematics and Computation, 268, 186-200 (2015) · Zbl 1410.34241 |
| [7] | Guan, Z. H.; Liu, Z. W.; Feng, G.; Wang, Y. W., Synchronization of complex dynamical networks with time-varying delays via impulsive distributed control, IEEE Transactions on Circuits and Systems. I. Regular Papers, 57, 8, 2182-2195 (2010) · Zbl 1468.93086 |
| [8] | He, D. X.; Ling, G.; Guan, Z. H.; Hu, B.; Liao, R. Q., Multisynchronization of coupled heterogeneous genetic oscillator networks via partial impulsive control, IEEE Transactions on Neural Networks and Learning Systems, 29, 2, 335-342 (2016) |
| [9] | He, W.; Qian, F.; Lam, J.; Chen, G.; Han, Q. L.; Kurths, J., Quasi-synchronization of heterogeneous dynamic networks via distributed impulsive control: Error estimation, optimization and design, Automatica, 62, 249-262 (2015) · Zbl 1330.93011 |
| [10] | Jain, A.; Dhar, J.; Gupta, V., Rumor model on homogeneous social network incorporating delay in expert intervention and government action, Communications in Nonlinear Science and Numerical Simulation, 84, Article 105189 pp. (2020) · Zbl 1450.91028 |
| [11] | Li, L.; Wang, X.; Li, C.; Feng, Y., Exponential synchronizationlike criterion for state-dependent impulsive dynamical networks, IEEE Transactions on Neural Networks and Learning Systems, 30, 4, 1025-1033 (2019) |
| [12] | Ling, G.; Guan, Z. H.; Chen, J.; Lai, Q., Chaotifying stable linear complex networks via single pinning impulsive strategy, International Journal of Bifurcation and Chaos, 29, 02, Article 1950024 pp. (2019) · Zbl 1414.34048 |
| [13] | Ling, G.; Guan, Z.; He, D.; Liao, R.; Zhang, X., Stability and bifurcation analysis of new coupled repressilators in genetic regulatory networks with delays, Neural Networks, 60, 222-231 (2014) · Zbl 1368.92058 |
| [14] | Ling, G.; Guan, Z. H.; Liao, R. Q.; Cheng, X. M., Stability and bifurcation analysis of cyclic genetic regulatory networks with mixed time delays, SIAM Journal on Applied Dynamical Systems, 14, 1, 202-220 (2015) · Zbl 1418.34068 |
| [15] | Lu, J.; Ho, D. W.; Cao, J., A unified synchronization criterion for impulsive dynamical networks, Automatica, 46, 7, 1215-1221 (2010) · Zbl 1194.93090 |
| [16] | Lu, J.; Kurths, J.; Cao, J.; Mahdavi, N.; Huang, C., Synchronization control for nonlinear stochastic dynamical networks: Pinning impulsive strategy, IEEE Transactions on Neural Networks and Learning Systems, 23, 2, 285-292 (2011) |
| [17] | Oc, S.; Eraslan, S.; Kirdar, B., Dynamic transcriptional response of saccharomyces cerevisiae cells to copper, Scientific Reports, 10, 18487 (2020) |
| [18] | Ouyang, D.; Shao, J.; Jiang, H.; Nguang, S. K.; Shen, H. T., Impulsive synchronization of coupled delayed neural networks with actuator saturation and its application to image encryption, Neural Networks, 128, 158-171 (2020) · Zbl 1471.93147 |
| [19] | Pan, L., Stochastic quasi-synchronization of delayed neural networks: Pinning impulsive scheme, Neural Processing Letters, 51, 947-962 (2020) |
| [20] | Pan, L.; Cao, J., Exponential stability of impulsive stochastic functional differential equations, Journal of Mathematical Analysis & Applications, 382, 2, 672-685 (2011) · Zbl 1222.60043 |
| [21] | Pan, L.; Cao, J., Stochastic quasi-synchronization for delayed dynamical networks via intermittent control, Communications in Nonlinear Science and Numerical Simulation, 17, 3, 1332-1343 (2012) · Zbl 1239.93114 |
| [22] | Pan, L.; Cao, J.; Al-Juboori, U. A.; Abdel-Aty, M., Cluster synchronization of stochastic neural networks with delay via pinning impulsive control, Neurocomputing, 366, 109-117 (2019) |
| [23] | Sivaranjani, K.; Rakkiyappan, R., Delayed impulsive synchronization of nonlinearly coupled Markovian jumping complex dynamical networks with stochastic perturbations, Nonlinear Dynamics, 88, 3, 1917-1934 (2017) · Zbl 1380.34034 |
| [24] | Sun, B.; Wang, S.; Cao, Y.; Guo, Z.; Wen, S., Exponential synchronization of memristive neural networks with time-varying delays via quantized sliding-mode control, Neural Networks, 126, 163-169 (2020) · Zbl 1471.93228 |
| [25] | Tang, Y.; Leung, S. Y.S.; Wong, W. K.; Fang, J. A., Impulsive pinning synchronization of stochastic discrete-time networks, Neurocomputing, 73, 10-12, 2132-2139 (2010) |
| [26] | Wang, Y.; Cao, J.; Hu, J., Stochastic synchronization of coupled delayed neural networks with switching topologies via single pinning impulsive control, Neural Computing and Applications, 26, 7, 1739-1749 (2015) |
| [27] | Wang, X.; Liu, X.; She, K.; Zhong, S., Pinning impulsive synchronization of complex dynamical networks with various time-varying delay sizes, Nonlinear Analysis. Hybrid Systems, 26, 307-318 (2017) · Zbl 1379.34049 |
| [28] | Wang, Y.; Lu, J.; Li, X.; Liang, J., Synchronization of coupled neural networks under mixed impulsive effects: A novel delay inequality approach, Neural Networks, 127, 38-46 (2020) · Zbl 1471.93231 |
| [29] | Wang, P.; Wang, W.; Su, H.; Feng, J., Stability of stochastic discrete-time piecewise homogeneous markov jump systems with time delay and impulsive effects, Nonlinear Analysis. Hybrid Systems, 38, Article 100916 pp. (2020) · Zbl 1478.93724 |
| [30] | Wang, F.; Yang, Y., Quasi-synchronization for fractional-order delayed dynamical networks with heterogeneous nodes, Applied Mathematics and Computation, 339, 1-14 (2018) · Zbl 1428.93013 |
| [31] | Wang, F.; Yang, Y., Quasi-projective synchronization of fractional order chaotic systems under input saturation, Physica A. Statistical Mechanics and its Applications, 534, 122-132 (2019) · Zbl 07570661 |
| [32] | Wang, Y. W.; Yang, W.; Xiao, J. W.; Zeng, Z. G., Impulsive multisynchronization of coupled multistable neural networks with time-varying delay, IEEE Transactions on Neural Networks and Learning Systems, 28, 7, 1560-1571 (2016) |
| [33] | Wang, L.; Zeng, Z.; Ge, M.; Hu, J., Global stabilization analysis of inertial memristive recurrent neural networks with discrete and distributed delays, Neural Networks, 105, 65-74 (2018) · Zbl 1441.93255 |
| [34] | Wei, F.; Chen, G.; Wang, W., Finite-time synchronization of memristor neural networks via interval matrix method, Neural Networks, 127, 7-18 (2020) · Zbl 1471.93240 |
| [35] | Wu, X.; Yan, L.; Zhang, W.; Tang, Y., Exponential stability of stochastic differential delay systems with delayed impulse effects, Journal of Mathematical Physics, 52, 9, Article 092702 pp. (2011) · Zbl 1272.82029 |
| [36] | Xiao, M.; Zheng, W. X.; Jiang, G.; Cao, J., Stability and bifurcation analysis of arbitrarily high-dimensional genetic regulatory networks with hub structure and bidirectional coupling, IEEE Transactions on Circuits and Systems. I. Regular Papers, 63, 8, 1-12 (2016) · Zbl 1468.94271 |
| [37] | Xu, Y.; Yang, H.; Tong, D.; Wang, Y., Adaptive exponential synchronization in \(p\) th moment for stochastic time varying multi-delayed complex networks, Nonlinear Dynamics, 73, 3, 1423-1431 (2013) · Zbl 1281.93112 |
| [38] | Yang, X.; Lam, J.; Ho, D. W.C.; Feng, Z., Fixed-time synchronization of complex networks with impulsive effects via non-chattering control, IEEE Transactions on Automatic Control, 62, 11, 5511-5521 (2017) · Zbl 1390.93393 |
| [39] | Yang, Z.; Xu, D., Stability analysis and design of impulsive control systems with time delay, IEEE Transactions on Automatic Control, 52, 8, 1448-1454 (2007) · Zbl 1366.93276 |
| [40] | Yao, J.; Su, Y.; Guo, Y.; Zhang, J., Exponential synchronisation of hybrid impulsive and switching dynamical networks with time delays, IET Control Theory & Applications, 7, 4, 508-514 (2013) |
| [41] | Yosef, N.; Regev, A., Impulse control: Temporal dynamics in gene transcription, Cell, 144, 6, 886-896 (2011) |
| [42] | Yu, J.; Hu, C.; Jiang, H.; Fan, X., Projective synchronization for fractional neural networks, Neural Networks, 49, 87-95 (2014) · Zbl 1296.34133 |
| [43] | Yue, D.; Guan, Z. H.; Li, J.; Liu, F.; Ling, G., Stability and bifurcation of delay-coupled genetic regulatory networks with hub structure, Journal of the Franklin Institute, 356, 5, 2847-2869 (2019) · Zbl 1411.92125 |
| [44] | Zhang, W.; Li, C.; He, X.; Li, H., Finite-time synchronization of complex networks with non-identical nodes and impulsive disturbances, Modern Physics Letters B, 32, 1, Article 1850002 pp. (2017) |
| [45] | Zhang, W.; Tang, Y.; Fang, J. A.; Zhu, W., Exponential cluster synchronization of impulsive delayed genetic oscillators with external disturbances, Chaos, 21, 4, 6-12 (2011) · Zbl 1317.34070 |
| [46] | Zhang, W.; Tang, Y.; Liu, Y.; Kurths, Jürgen, Event-triggering containment control for a class of multi-agent networks with fixed and switching topologies, IEEE Transactions on Circuits and Systems. I. Regular Papers, 64, 3, 619-629 (2017) |
| [47] | Zhang, W.; Tang, Y.; Wu, X.; Fang, J. A., Synchronization of nonlinear dynamical networks with heterogeneous impulses, IEEE Transactions on Circuits and Systems. I. Regular Papers, 61, 4, 1220-1228 (2017) |
| [48] | Zhou, Y.; Zeng, Z., Event-triggered impulsive control on quasi-synchronization of memristive neural networks with time-varying delays, Neural Networks, 110, 55-65 (2019) · Zbl 1441.93188 |
| [49] | Zhu, S.; Zhou, J.; Lyu, J.; Lu, J. A., Finite-time synchronization of impulsive dynamical networks with strong nonlinearity, IEEE Transactions on Automatic Control (2020) |
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