Previous |  Up |  Next

Article

Keywords:
prescribed-time; outer synchronization; drive-response systems; pinning control; noise
Summary:
This paper investigates prescribed-time outer synchronization in drive-response complex networks with the perturbation of noise. We propose two control frameworks: a general prescribed-time controller and its pinning control variant. Through the stability theory of stochastic differential equations, we establish sufficient conditions that ensure outer synchronization in drive-response systems within a prescribed finite convergence time, independent of both initial conditions and system parameters. The proposed controllers are shown to be continuous and bounded. Numerical simulations demonstrate the effectiveness and feasibility of the proposed control schemes.
References:
[1] Barabási, A.-L.: Scale-free networks: A decade and beyond. Science 325 (2009), 412-413. DOI 
[2] Čelikovský, S., Lynnyk, V., Lynnyk, A., Rehak, B.: Generalized synchronization in the networks with directed acyclic structure. Kybernetika 59 (2023), 437-460. DOI 
[3] Chen, W., Jiao, L. C.: Finite-time stability theorem of stochastic nonlinear systems. Automatica 46 (2010), 2105-2108. DOI 
[4] Chen, J., Li, X., Wu, X., Shen, G.: Prescribed-time synchronization of complex dynamical networks with and without time-varying delays. IEEE Trans. Netw. Sci. Eng. 9 (2022), 4017-4027. DOI 
[5] Klovdahl, A. S.: Social networks and the spread of infectious diseases: The AIDS example. Soc. Sci. Med. 21 (1985), 1203-1216. DOI 
[6] Lai, Q., Guo, S.: Heterogeneous coexisting attractors, large-scale amplitude control and finite-time synchronization of central cyclic memristive neural networks. Neural Networks 178 (2024), 106412. DOI 
[7] Li, M., Zhao, D., Sun, R., Sun, Y.: Time and energy costs for stochastic synchronisation of multi-layer complex networks with noise. Int. J. Control 98 (2025), 934-943. DOI 
[8] Li, X., Wang, N., Lu, J., Alsaadi, F. E.: Pinning outer synchronization of partially coupled dynamical networks with complex inner coupling matrices. Physica A 515 (2019), 497-509. DOI 
[9] Ma, Z.-C., Wu, J., Sun, Y.-Z.: Adaptive finite-time generalized outer synchronization between two different dimensional chaotic systems with noise perturbation. Kybernetika \textit{53} (2017), 838-852. DOI 
[10] Moiseff, A., Copeland, J.: Firefly synchrony: a behavioral strategy to minimize visual clutter. Science 329 (2010), 181-181. DOI 
[11] Néda, Z., Ravasz, E., Brechet, Y., Vicsek, T., Barabási, A.-L.: The sound of many hands clapping. Nature 403 (2000), 849-850. DOI 
[12] Platen, E., Bruti-Liberati, N.: Numerical Solution of Stochastic Differential Equations With Jumps in Finance. Springer, Berlin 2010.
[13] Pu, H., Li, F.: Fixed/predefined-time synchronization of complex-valued discontinuous delayed neural networks via non-chattering and saturation control. Physica A 610 (2023), 128425. DOI 
[14] Qian, Y.: Finite-time topological identification of complex network with time delay and stochastic disturbance. Kybernetika 57 (2021), 534-545. DOI 
[15] Song, Y., Wang, Y., Holloway, J., Krstic, M.: Time-varying feedback for regulation of normal-form nonlinear systems in prescribed finite time. Automatica 83 (2017), 243-251. DOI 
[16] Sun, Y., Zhao, D.: Effects of noise on the outer synchronization of two unidirectionally coupled complex dynamical networks. Chaos 22 (2012), 023131. DOI 
[17] Sun, F., Wu, X., Kurths, J., Zhu, W.: Group consensus for heterogeneous multiagent systems with time delays based on frequency domain approach. IEEE Trans. Syst., Man, Cybernet.: Syst. 53 (2023), 2572-2582. DOI 
[18] Sun, Y., Li, W., Zhao, D.: Finite-time stochastic outer synchronization between two complex dynamical networks with different topologies. Chaos 22 (2012), 023152. DOI 
[19] Sun, Y.-Z., Li, W., Ruan, J.: Finite-time generalized outer synchronization between two different complex networks. Commun. Theor. Phys. 58 (2012), 697. DOI  | Zbl 1264.05128
[20] Tan, F., Zhou, L., Chu, Y., Li, Y.: Fixed-time stochastic outer synchronization in double-layered multi-weighted coupling networks with adaptive chattering-free control. Neurocomputing 399 (2020), 8-17. DOI 
[21] Tan, F., Zhou, L., Lu, J., Chu, Y., Li, Y.: Fixed-time outer synchronization under double-layered multiplex networks with hybrid links and time-varying delays via delayed feedback control. Asian J. Control 24 (2022), 137-148. DOI 10.1002/asjc.2420
[22] Wang, X.-F., Chen, G.-R.: Pinning control of scale-free dynamical networks. Physica A 310 (2002), 521-531. DOI  | Zbl 0995.90008
[23] Wang, J., Liu, J., Zheng, Y., Xi, J.: Analysis of $H_{\infty}$ performance for multi-agent networks. IEEE Trans. Automat. Control 69 (2024), 5125-5140. DOI 
[24] Wang, Y., Song, Y., Hill, D. J., Krstic, M.: Prescribed-time consensus and containment control of networked multiagent systems. IEEE Trans. Cybern. 49 (2019), 1138-1147. DOI 
[25] Wang, C.-Y., Zhang, J.-Q., Wu, Z.-X., Guan, J.-Y.: Collective firing patterns of neuronal networks with short-term synaptic plasticity. Phys. Rev. E 103 (2021), 022312. DOI 10.1103/PhysRevE.103.022312
[26] Wang, J., Zhang, J., Yuan, Z., Chen, A., Zhou, T.: Neurotransmitter-mediated collective rhythms in grouped drosophila circadian clocks. J. Biol. Rhythms 23 (2008), 472-482. DOI 
[27] Watts, D. J., Strogatz, S. H.: Collective dynamics of ‘small-world’ networks. Nature 393 (1998), 440-442. DOI 
[28] Wu, Y., Guo, H., Xue, L., Gunasekaran, N., Liu, J.: Prescribed-time synchronization of stochastic complex networks with high-gain coupling. IEEE Trans. Circuits Syst. II: Express Briefs 70 (2023), 4133-4137. DOI 
[29] Wu, J., Sun, Y.-Z., Zhao, D.-H.: Finite-time adaptive outer synchronization between two complex dynamical networks with nonidentical topological structures. Kybernetika 51 (2015), 655-666. DOI  | Zbl 1340.34181
[30] Wu, X., Wu, X., Wang, C.-Y., Mao, B., Lu, J.-A., Lu, J., Zhang, Y.-C., Lu, L.: Synchronization in multiplex networks. Physics Reports 1060 (2024), 1-54. DOI 
[31] Yu, W., Lü, J., Yu, X., Chen, G.: Distributed adaptive control for synchronization in directed complex networks. SIAM J. Control Optim. 53 (2015), 2980-3005. DOI 
[32] Zhang, M., Huang, T., Guo, Z., He, Z.: Complex-network-based traffic network analysis and dynamics: A comprehensive review. Physica A 607 (2022), 128063. DOI 
[33] Zhang, H., Yan, X.: Prescribed-time synchronization of Kuramoto oscillators over undirected network. IEEE Trans. Circuits Syst. II: Express Briefs 71 (2024), 3041-3045. DOI 
[34] Zhang, X., Zhu, Y., Zheng, Y.: Generalized synchronization-based partial topology identification of complex networks. Kybernetika 59 (2023), 512-526. DOI 
Partner of
EuDML logo