Abstract
Global asymptotic synchronization problem of a coupled interconnected recurrent neural networks with linearly delayed coupled has been investigated. By using the state feedback and delayed state feedback pinning control method, two different pinning synchronization criteria have been established. One is based on the matrix eigenvalue of the coupled matrix, the other is based on the matrix inequality of the known networks information. Some remarks on the synchronization criteria are used to show the characteristics of the proposed results.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Watts, D., Strogatz, S.: Collective dynamics of small-world networks. Nature 393, 440–442 (1998)
Pecora, L., Carroll, T.: Master stability function for synchronized coupled systems. Phys. Rev. Lett. 80, 2109–2112 (1998)
Wu, C., Chua, L.: Synchronization in an array of linearly coupled dynamical systems. IEEE Trans. Circ. Syst-I 42, 430–447 (1995)
Pastor-Satorras, R., Vespignani, A.: Epidemic spread in scale-free networks. Phys. Rev. Lett. 86, 3200–3203 (2001)
Wang, X., Chen, G.: Synchronization in scale-free dynamical networks: robustness and fragility. IEEE Trans. Circ. Syst-I 49, 54–62 (2002)
Zhou, J., Chen, T.: Synchronization in general complex delayed dynamical networks. IEEE Trans. Circ. Syst-I 53, 733–744 (2006)
Lu, J., Yu, X., Chen, G.: Chaos synchronization of general complex dynamical networks. Physica A 33, 281–302 (2004)
Wu, J., Jiao, L.: Synchronization in complex dynamical networks with nonsymmetric coupling. Physica D 237, 2487–2498 (2008)
Zhan, M., Gao, J., Wu, Y.: Chaos synchronization in coupled systems by applying pinning control. Phys. Rev. E 76, 036203 (2007)
Wang, X., Chen, G.: Pinning control of scale-free dynamical networks. Physica A 310, 521–531 (2002)
Li, X., Wang, X., Chen, G.: Pinning a complex dynamical network to its equilibrium. IEEE Trans. Circ. Syst-I 51, 2074–2087 (2004)
Chen, T., Liu, X., Lu, W.: Pinning complex networks by a single controller. IEEE Trans. Circ. Syst-I 54, 1317–1326 (2007)
Zhou, J., Wu, Q., Xiang, L.: Pinning complex delayed dynamical networks by a single impulse controller. IEEE Trans. Circ. Syst-I 58, 1–12 (2011)
Zhou, J., Wu, X., Yu, W.: Pinning synchronization of delayed neural networks. Chaos 18, 043111 (2008)
Zhao, J., Lu, J., Zhang, Q.: Pinning a complex delayed dynamical network to a homogenous trajectory. IEEE Trans. Circ. Syst-II 56, 514–517 (2009)
Guo, W., Austin, F., Chen, S.: Pinning synchronization of the complex networks with non-delayed and delayed coupling. Phys. Lett. A 373, 1565–1572 (2009)
Lu, J., Yu, X., Chen, G.: Chaos synchronization of general complex dynamical networks. Phys. A 334, 281–302 (2004)
Lu, J., Chen, G.: A time-varying complex dynamical network models and its controlled synchronization criteria. IEEE Trans. Autom. Control 50, 841–846 (2005)
Zhao, J., Lu, J., Wu, X.: Pinning control of general complex dynamical networks with optimization. Science China - Information Sciences 53, 813–822 (2010)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Wang, Z., Zhou, D., Ma, D., Lun, S. (2012). Global Asymptotic Synchronization of Coupled Interconnected Recurrent Neural Networks via Pinning Control. In: Wang, J., Yen, G.G., Polycarpou, M.M. (eds) Advances in Neural Networks – ISNN 2012. ISNN 2012. Lecture Notes in Computer Science, vol 7367. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31346-2_34
Download citation
DOI: https://doi.org/10.1007/978-3-642-31346-2_34
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-31345-5
Online ISBN: 978-3-642-31346-2
eBook Packages: Computer ScienceComputer Science (R0)