A Brief Survey on Finite Time and Fixed
Time Synchronization of Complex Dynamical
Networks and its applications

K S Anand; S. Padmanabhan; G A Harish Babu; Brinda R

doi:https://doi.org/10.14445/22315373/IJMTT-V66I4P520

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 66 | Issue 4 | Year 2020 | Article Id. IJMTT-V66I4P520 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I4P520

A Brief Survey on Finite Time and Fixed Time Synchronization of Complex Dynamical Networks and its applications

K S Anand, S. Padmanabhan, G A Harish Babu, Brinda R

Abstract

Complex networks have, in recent years, brought many innovative impacts to large-scale systems. However, great challenges also come forth due to distinct complex situations and imperative requirements in human life now a days. This paper attempts to present an overview of recent progress of synchronization of complex dynamical networks and its applications. We focus on Finite-time and Fixed-time synchronization of complex dynamical networks with nonidentical discontinuous nodes, time delay, Class of Output-Coupling via continuous control and Markovian jump complex networks. Then, were view several applications of synchronization in complex networks, especially in neuroscience and power grids. The present limitations are summarized and future trends are explored and tentatively highlighted.

Keywords

Complex network, synchronization, finite-time and fixed-time, coupling, time delay, impulsive, adaptive, intermittent, Markovian jump.

References

[1] G. Chen and Z. Duan, “Network synchronizability analysis: a graph-theoretic approach,” Chaos. An Interdisciplinary Journal of Nonlinear Science, vol. 18, No. 3, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
[2] C. W. Wu and L. O. Chua, “Synchronization in an array of linearly coupled dynamical systems”, IEEE Transactions on Circuits and Systems. I. Fundamental Theory and Applications, vol. 42, No. 8, pp. 430–447, 1995.
[3] W. Lu and T. Chen, “New approach to synchronization analysis of linearly coupled ordinary differential systems,” Physics D. Nonlinear Phenomena, vol. 213, no. 2, pp. 214–230, 2006.
[4] Z. Li and J.-J. Lee, “New Eigen value based approach to synchronization in asymmetrically coupled networks,” Chaos. An Interdisciplinary Journal of Nonlinear Science, vol. 17, no. 4, Article ID 043117, 2007.
[5] Yu, W.W., Chen, G.R. and Lv, J.H. (2009) On Pinning Synchronization of Complex Dynamical Networks. Automatica, 45, 429-435 https://doi.org/10.1016/j.automatica.2008.07.016.
[6] Zhang, W., Li, C., Huang, T. and He, X. (2015) Synchronization of Memristor-Based Coupling Recurrent Neural Networks with Time-Varying Delays and Impulses. IEEE Transactions on Neural Networks and Learning Systems, 26, 3308-3313. https://doi.org/10.1109/TNNLS.2015.2435794
[7] Han, F., Wei, G.L., Ding, D.R. and Song, Y. (2017) Finite-Horizon Bounded H Synchronisation and State Estimation for Discrete- Time Complex Networks: Local Performance Analysis. IET Control Theory and Applications, 11, 827-837. https://doi.org/10.1049/iet-cta.2016.1161.
[8] Shen, B., Wang, Z.D., Ding, D.R. and Shu, H.S. (2013) H-Infinity State Estimation for Complex Networks with Uncertain Inner Coupling and Incomplete Measurements. IEEE Transactions on Neural Networks and Learning Systems, 24, 2027-2037. https://doi.org/10.1109/TNNLS.2013.2271357.
[9] Wu, W., Zhou, W.J. and Chen, T.P. (2009) Cluster Synchronization of Linearly Coupled Complex Networks under Pinning Control. IEEE Transactions on Circuits and Systems I: Regular Papers, 56, 829-839. https://doi.org/10.1109/TCSI.2008.2003373.
[10] Lam, H. and Leung, F. (2006) Synchronization of Uncertain Chaotic Systems Based on the Fuzzy-Model-Based Approach. International Journal of Bifurcation and Chaos, 16, 1435-1444. https://doi.org/10.1142/S0218127406015404
[11] Guan, Z., Liu, Z., Feng, G. and Wang, Y. (2010) Synchronization of Complex Dynamical Networks with Time-Varying Delays via Impulsive Distributed Control. IEEE Transactions on Circuits and Systems I: Regular Papers, 57, 2182-2195. https://doi.org/10.1109/TCSI.2009.2037848.
[12] Zhang, L., Yang, X.S., Chen, X. and Feng, J.W. (2017) Exponential Synchronization of Complex-Valued Complex Networks with Time-Varying Delays and Stochastic Perturbations Via Time-Delayed Impulsive Control. Applied Mathematics and Computation, 306, 22-30. https://doi.org/10.1016/j.amc.2017.02.004
[13] Bao, H., Park, J. And Cao, J. (2016) Exponential Synchronization of Coupled Stochastic Memristor-Based Neural Networks with Time-Varying Probabilistic Delay Coupling and Impulsive Delay. IEEE Transactions on Neural Networks and Learning Systems, 27, 190-201. https://doi.org/10.1109/TNNLS.2015.2475737
[14] Yang, X., Wu, Z. and Cao, J.D. (2013) Finite-Time Synchronization of Complex Networks with Nonidentical Discontinuous Nodes. Nonlinear Dynamics, 73, 2313-2327. https://doi.org/10.1007/s11071-013-0942-4
[15] Jiang, S.Q., Lu, X.B., Xie, C. and Cai, S.M. (2017) Adaptive Finite-Time Control for Overlapping Ciuster Synchronization in Coupled Complex Networks. Neurocomputing, 266, 188-195. https://doi.org/10.1016/j.neucom.2017.05.031.
[16] Mei, J., Jiang, M., Wu, Z. and Wang, X. (2015) Periodically Intermittent Controlling for Finite-Time Synchronization of Complex Dynamical Networks. Nonlinear Dynamics, 79, 295-305. https://doi.org/10.1007/s11071-014-1664-y
[17] Liu, M., Jiang, H.J. and Hu, C. (2017) Finite-Time Synchronization of Delayed Dynamical Networks via Aperiodically Intermittent Control. Journal of the Franklin Institute, 4, 5374-5397. https://doi.org/10.1016/j.jfranklin.2017.05.030
[18] Liu, X.W. and Chen, T.P. (2018) Finite-Time and Fixed-Time Cluster Synchronization with or without Pinning Control. IEEE Transactions on Cybernetics, 48, 950-955. https://doi.org/10.1109/TCYB.2016.2630703.
[19] Chen WH, Luo S, Zheng WX (2016) Impulsive synchronization of reaction–diffusion neural networks with mixed delays and its application to image encryption. IEEE Trans Neural Network Learn Syst 27(12):2696–2710.
[20] Tengda Wei et al (2019), Adaptive synchronization of stochastic complex dynamical networks and its application, Neural Computing and Applications, vol.31, 6879–6892 https://doi.org/10.1007/s00521-018-3501-6.
[21] Wu, W., Zhou, W.J. and Chen, T.P. (2009) Cluster Synchronization of Linearly Coupled Complex Networks under Pinning Control. IEEE Transactions on circuits and systems I: Regular Papers, 56, 829-839.
[22] Lu, W. L. and Chen, T.P. (2004) Synchronization of Coupled Connected Neural Networks with Delays. IEEE Transactions on circuits and systems I: Regular Papers, 51, 2494-2503. https://doi.org/10.1109/TCSI.2004.838308.
[23] Chen, T.P., Liu, X.W. and Lu, W.L. (2007) Pinning Complex Networks by a Single Controller. IEEE Transactions on circuits and systems I: Regular Papers, 54, 1317- 1326. https://doi.org/10.1109/TCSI.2007.895383
[24] Liu, X. and Chen, T. (2015) Fixed-Time Cluster Synchronization for Complex Net- works via Pinning Control. arXiv:1509.03350.
[25] Lu, W.L. and Chen, T.P. (2004) Synchronization of Coupled Connected Neural Networks with Delays. IEEE Transactions on Circuits and Systems I: Regular Papers, 51, 2494-2503.
[26] Chen, T.P., Liu, X.W. and Lu, W.L. (2007) Pinning Complex Networks by a Single Controller. IEEE Transactions on Circuits and Systems I: Regular Papers, 54, 1317-1326. https://doi.org/10.1109/TCSI.2007.895383.
[27] Liu, X.W. and Chen, T.P. (2018) Finite-Time and Fixed-Time Cluster Synchronization with or without Pinning Control. IEEE Transactions on cybernetics 48, 950-955. https://doi.org/10.1109/TCYB.2016.2630703.
[28] Yang, X. and Cao, J. (2010) Finite-Time Stochastic Synchronization of Complex Networks. Applied Mathematical Modelling, 34, 3631-3641. https://doi.org/10.1016/j.apm.2010.03.012
[29] A. Stoica, I. Yaesh, Markovian jump delayed Hopfield networks with multiplicative noise, Automatica 44 (8) (2008) 2157–2162.
[30] Y. Tang, W.K. Wong, Distributed synchronization of coupled neural networks via randomly occurring control, IEEE Trans. Neural Netw. and Learn. Syst. 24 (2013) 435–447.
[31] Y. Liu, Z. Wang, X. Liu, Exponential synchronization of complex networks with Markovian jump and mixed delays, Phys. Lett. A 372 (2008) 3986–3998.
[32] J.J. Hopfield, Neurons with graded response have collective computational properties like those of twostate neurons, Proc. Natl. Acad. Sci. USA 81 (1984) 3088–3092.
[33] Y. Tang, H. Gao, W. Zou, J. Kurths, Distributed synchronization in networks of agent systems with nonlinearities and random switchings, IEEE Trans. Cybern. 43 (1) (2013) 358–370.
[34] X. Yang, J. Cao, J. Lu, Synchronization of Markovian coupled neural networks with nonidentical node-delays and random coupling strengths, IEEE Trans. Neural Netw. Learn. Syst. 23 (1) (2012) 60–71.
[35] W. Zhang, J. Fang, Y. Tang, Stochastic stability of Markovian jumping genetic regulatory networks with mixed time delays, Appl. Math. Comput. 217 (2011) 7210–7225.
[36] Z. Wu, P. Shi, H. Su, J. Chu, Passivity analysis for discrete-time stochastic Markovian jump neural networks with mixed time delays, IEEE Trans. Neural Netw. 22 (10) (2011) 1566–1575.
[37] Y. Zhu, H. Qi, D. Cheng, Synchronisation of a class of networked passive systems with switching topology, Int. J.Control 82 (7) (2009) 1326–1333.
[38] Y. Liu, Z. Wang, Stability and synchronization of discrete-time Markovian jumping neural networks with mixed mode-dependent time delays, IEEE Trans. Neural Netw. 20 (7) (2009) 1102–1116.
[39] J. Xiang, W. Wei, On local synchronisability of nonlinear networked systems with a unit inner-coupling matrix and switching topology, Int. J. Control 84 (11) (2011) 1769–1778.

Citation :

K S Anand, S. Padmanabhan, G A Harish Babu, Brinda R, "A Brief Survey on Finite Time and Fixed Time Synchronization of Complex Dynamical Networks and its applications," International Journal of Mathematics Trends and Technology (IJMTT), vol. 66, no. 4, pp. 149-171, 2020. Crossref, https://doi.org/10.14445/22315373/IJMTT-V66I4P520