Abstract
Based on feedback control, a problem is discussed in which the state variables of nodes of general complex delayed dynamical networks are controlled to its equilibrium. The delay differential inequality is employed to investigate delay-dependent of this system and some sufficient conditions for asymptotic stability are presented. At the same time, they provide concrete bounds of the delays in terms of explicit expression. A scale-free network is discussed in numerical simulations. They show the effectiveness and feasibility of the proposed conditions.
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References
Watts, D.J., Strogatz, S.H.: Collective Dynamics of Small-world. Nature 393, 440–442 (1998)
Barabasi, A.L., Albert, R.: Emergence of Scaling in Random Networks. Science 286, 509–512 (1999)
Newman, M.E.J.: The Structure and Function of Complex Networks. SIAM Rev. 45(2), 167–256 (2003)
Wang, X.F., Li, X., Chen, G.R.: Theory and Application of the Complex Networks. Qinghua university press, Beijing (2006)
Wang, X.F., Chen, G.: Pinning Control of Scale-free Dynamical Networks. Physica A 310, 521–531 (2002)
Li, X., Wang, X.F., Chen, G.: Pinning a Complex Dynamical Network to Its Equilibrium. IEEE Trans. Circuits Syst. -I 51(10), 2074–2087 (2004)
Fan, Z.P., Chen, G.: Pinning Control of Scale-free Complex Networks. In: Proceedings of the IEEE ISCAS 2005 Kobe, Japan, pp. 284–287 (2005)
Chen, G., Fan, Z.P.: Modelling, Control and Synchronization of Complex Networks. In: Proceedings of 2005 Chinese Control and Decision Conference, pp. 22–31 (2005)
Li, X., Wang, X.F.: Feedback Control of Scal-free Coupled Henon maps. In: Proceeding of the Eighth International Conference on control, Automation, Robotics and Vision at Kumming, China, pp. 574–578 (2004)
Albert, R., Jeong, H., Barabśi, A.-L.: Error and Attack Tolerance of Complex Networks. Nature 406, 378–482 (2000)
Albert, R., Barabsi, A.L.: Statistical Mechanics of Complex Networks. Rev. Mod. Phys. 74, 47–97 (2002)
Wang, X.F.: Complex Networks: Topology, Dynamics and Synchronization. International Journal of Bifurcation & Chaos 12(5), 885–916 (2002)
Wang, X., Chen, G.: Synchronization in Scale-free Dynamical Networks: Robustness and Fragility. IEEE Trans.on Circuits and Systems 49(1), 54–62 (2002)
Zhou, J., Lu, J.A., Lu, J.H.: Adaptive Synchronization of an Uncertain Complex Dynamical Network. IEEE Transactions on Automatic Control 51(4), 652–656 (2006)
Chen, J.Y., Wong, K.W., Shuai, J.W.: Phase Synchronization in Coupled Chaotic Oscillators with Time Delay. Phys. Rev. E 66, 56–203 (2002)
Lu, W., Chen, T.: Synchronization of Coupled Connected Neural Networks with Delays. IEEE Trans. Circuits Syst. I 51, 2491–2503 (2004)
Tu, L.L., Lu, J.A.: Stability of a Model for a Delayed Genetic Regulatory Network, Dynamics of Continuous. Discrete and Impulsive Systems 13, 429–439 (2006)
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Tu, L. (2009). Feedback Control in General Complex Delayed Dynamical Networks. In: Yu, W., He, H., Zhang, N. (eds) Advances in Neural Networks – ISNN 2009. ISNN 2009. Lecture Notes in Computer Science, vol 5552. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01510-6_114
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DOI: https://doi.org/10.1007/978-3-642-01510-6_114
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