Graph-theoretic approach to exponential stability of delayed coupled systems on networks under periodically intermittent control
Abstract
In this paper, the exponential stability of delayed coupled systems on networks (DCSNs) is investigated via periodically intermittent control. By utilizing graph-theoretic approach and Lyapunov function method, a novel method for stability analysis of DCSNs is developed. Moreover, some useful and easily verifiable sufficient conditions are presented in the form of Lyapunov-type theorem and coefficients-type criterion. These laws reveal that the stability has a close relationship with the topology structure of the networks. In addition, as a subsequent result, the obtained theory is successfully applied to study the exponential stability of delayed coupled oscillators on networks under periodically intermittent control. Finally, a numerical example is given to validate the effectiveness of theoretical results.
Keyword : delayed coupled systems, periodically intermittent control, graph-theoretic method, exponential stability
How to Cite
Guo, B., Xiao, Y., & Zhang, C. (2018). Graph-theoretic approach to exponential stability of delayed coupled systems on networks under periodically intermittent control. Mathematical Modelling and Analysis, 23(1), 44-63. https://doi.org/10.3846/mma.2018.004
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
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H. Su, W. Li, K. Wang and X. Ding. Stability analysis for stochastic neural network with infinite delay. Neurocomputing, 74(10):1535–1540, 2011. https://doi.org/10.1016/j.neucom.2010.12.027
H. Su, P. Wang and X. Ding. Stability analysis of discrete-time coupled systems with multi-diffusion by graph-theoretic approach and its applications. Discrete Contin. Dyn. Syst-Ser. B, 21:253–269, 2016.
J. Suo, J. Sun and Y. Zhang. Stability analysis for impulsive coupled systems on networks. Neurocomputing, 99:172–177, 2013. https://doi.org/10.1016/j.neucom.2012.06.002
P. Venkataram, S. Ghosal and B.P.V. Kumar. Neural network based optimal routing algorithm for communication networks. Neural Netw., 15(10):1289–1298, 2002. https://doi.org/10.1016/S0893-6080(02)00067-9
Z. Wang, Z. Duan and J. Cao. Impulsive synchronization of coupled dynamical networks with nonidentical duffing oscillators and coupling delays. Chaos, 22(1):013140, 2012. https://doi.org/10.1063/1.3692971
D. West. Introduction to graph theory. Prentice Hall, Upper Saddle River, 1996.
J. Xiao, G. Hu and Z. Qu. Synchronization of spatiotemporal chaos and its application to multichannel spread-spectrum communication. Phys. Rev. Lett., 77(20):4162–4165, 1996. https://doi.org/10.1103/PhysRevLett.77.4162
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J. Yu, C. Hu and H. Jiang. Exponential synchronization of Cohen-Grossberg neural networks via periodically intermittent control. Neurocomputing, 74(10):1776–1782, 2011. https://doi.org/10.1016/j.neucom.2011.02.015
C. Zhang, W. Li and K. Wang. Boundedness for network of stochastic coupled van der Pol oscillators with time-varying delayed coupling. Appl. Math. Model., 37(7):5394–5402, 2013. https://doi.org/10.1016/j.apm.2012.10.032
C. Zhang, W. Li and K. Wang. A graph-theoretic approach to stability of neutral stochastic coupled oscillators network with time-varying delayed coupling. Math. Meth. Appl. Sci., 37(8):1179–1190, 2014. https://doi.org/10.1002/mma.2879
C. Zhang, W. Li and K. Wang. Graph-theoretic method on exponential synchronization of stochastic coupled networks with Markovian switching. Nonlinear Anal.-Hybrid Syst., 15:37–51, 2015. https://doi.org/10.1016/j.nahs.2014.07.003
G. Zhang and Y. Shen. Exponential stability of memristor-based chaotic neural networks with time-varying delays via intermittent control. IEEE Trans. Neural Netw. Learn. Syst., 26(7):1431–1441, 2015. https://doi.org/10.1109/TNNLS.2014.2345125
J. Zhang and X. Guo. Stability and bifurcation analysis in the delay-coupled van der Pol oscillators. Appl. Math. Model., 34(9):2291–2299, 2010. https://doi.org/10.1016/j.apm.2009.10.037
W. Zhang, C. Li, T. Huang and J. Huang. Stability and synchronization of memristor-based coupling neural networks with time-varying delays via intermittent control. Neurocomputing, 173(Part 3):1066–1072, 2016. https://doi.org/10.1016/j.neucom.2015.08.063
X. Zhang, W. Li and K. Wang. The existence and global exponential stability of periodic solution for a neutral coupled system on networks with delays. Appl. Math. Comput., 264:208–217, 2015. https://doi.org/10.1016/j.amc.2015.04.109
C. Zhou and T. Chen. Digital communication robust to transmission error via chaotic synchronization based on contraction maps. Phys. Rev. Lett., 56(2):1599–1604, 1997. https://doi.org/10.1103/PhysRevE.56.1599