Abstract
We explore a process for identifying the topology of networks. We find that it is possible to estimate the accurate topological structure of synchronous networks by analyzing their transient processes. Some novel conditions are given to ensure the uncertain connection topology approach to the true value. Our examples further illustrate the feasibility of these proposed methods.
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References
Strogatz, S.H.: Exploring complex networks. Nature 410, 268–276 (2001)
Watts, D.J., Strogatz, S.H.: Collective dynamics of ’small-world’ networks. Nature 393, 440–442 (1998)
Wang, X., Guan, S., Lai, Y., Li, B., Lai, C.: Desynchronization and on-off intermittency in complex networks. Europhys. Lett. 88, 28001 (2009)
Ma, X., Huang, L., Lai, Y., Zheng, Z.: Emergence of loop structure in scale-free networks and dynamical consequences. Phys. Rev. E, Stat. Nonlinear Soft Matter Phys. 79, 056106 (2009)
Ren, J., Wang, W., Li, B., Lai, Y.: Noise bridges dynamical correlation and topology in coupled oscillator networks. Phys. Rev. Lett. 104, 058701 (2010)
Donner, R., Zou, Y., Donges, J., Marwan, N., Kurths, J.: Ambiguities in recurrence-based complex network representations of time series. Phys. Rev. E, Stat. Nonlinear Soft Matter Phys. 81, 015101 (2009)
Shang, Y., Chen, M., Kurths, J.: Generalized synchronization of complex networks. Phys. Rev. E, Stat. Nonlinear Soft Matter Phys. 80, 027201 (2009)
Ye, W., Huang, X., Huang, X., Li, P., Xia, Q., Hu, G.: Self-sustained oscillations of complex genomic regulatory networks. Phys. Lett. A 374, 2521–2526 (2010)
Yu, D., Righero, M., Kocarev, L.: Estimating topology of networks. Phys. Rev. Lett. 97, 188701 (2006)
Zhou, J., Lu, J.: Topology identification of weighted complex dynamical networks. Physica A 386, 481–491 (2007)
Wu, X.Q.: Synchronization-based topology identification of weighted general complex dynamical networks with time-varying coupling delay. Physica A 387, 997–1008 (2008)
Chen, L., Lu, J., Tse, C.: Synchronization: an obstacle to identification of network topology. IEEE Trans. Circuits Syst. II, Express Briefs 56, 310–314 (2009)
Zhao, J., Li, Q., Lu, J., Jiang, Z.: Topology identification of complex dynamical networks. Chaos 20, 023119 (2010)
Tang, W.K.S., Mao, Y., Kocarev, L.: Identification and monitoring of biological neural network. In: IEEE Int. Symp. Circuits Syst. Proc., pp. 2646–2649, May 27–30, 2007
Lu, J., Cao, J.: Synchronization-based approach for parameters identification in delayed chaotic neural networks. Physica A 382(2), 672–682 (2007)
Lou, X., Cui, B.: Synchronization of neural networks based on parameter identification and via output or state coupling. J. Comput. Appl. Math. 222(2), 440–457 (2008)
Parlitz, U.: Estimating model parameters from time series by autosynchronization. Phys. Rev. Lett. 76, 1232–1235 (1996)
Huang, D.: Synchronization-based estimation of all parameters of chaotic systems from time series. Phys. Rev. E, Stat. Nonlinear Soft Matter Phys. 69, 067201 (2004)
Huang, D.: Simple adaptive-feedback controller for identical chaos synchronization. Phys. Rev. E, Stat. Nonlinear Soft Matter Phys. 71, 037203 (2005)
Huang, D.: Adaptive-feedback control algorithm. Phys. Rev. E, Stat. Nonlinear Soft Matter Phys. 73, 066204 (2006)
Li, L., Peng, H., Wang, X., Yang, Y.: Comment on two papers of chaotic synchronization. Phys. Lett. A 333, 269–270 (2004)
Yu, D., Wu, A.: Comment on “Estimating model parameters from time series by autosynchronization”. Phys. Rev. Lett. 94, 219401 (2005)
Li, R., Xu, W., Li, S.: Adaptive generalized projective synchronization in different chaotic systems based on parameter identification. Phys. Lett. A 367, 199–206 (2007)
Yu, W., Chen, G., Cao, J., Lü, J., Parlitz, U.: Parameter identification of dynamical systems from time series. Phys. Rev. E, Stat. Nonlinear Soft Matter Phys. 75, 067201 (2007)
Yu, D., Parlitz, U.: Estimating parameters by autosynchronization with dynamics restrictions. Phys. Rev. E, Stat. Nonlinear Soft Matter Phys. 77, 066221 (2008)
Sun, F., Peng, H., Luo, Q., Li, L., Yang, Y.: Parameter identification and projective synchronization between different chaotic systems. Chaos 19, 023109 (2009)
Peng, H., Li, L., Yang, Y., Wang, C.: Parameter estimation of nonlinear dynamical systems based on integrator theory. Chaos 19, 033130 (2009)
Peng, H., Li, L., Yang, Y., Liu, F.: Parameter estimation of dynamical systems via a chaotic ant swarm. Phys. Rev. E, Stat. Nonlinear Soft Matter Phys. 81, 016207 (2010)
Peng, H., Li, L., Sun, F., Yang, Y., Li, X.: Parameter identification and synchronization of dynamical system by introducing an auxiliary subsystem. Adv. Differ. Equ. 2010, 808403 (2010)
Peng, H., Wei, N., Li, L., Xie, W., Yang, Y.: Models and synchronization of time-delayed complex dynamical networks with multi-links based on adaptive control. Phys. Lett. A 374, 2335–2339 (2010)
Astrom, K.J., Wittenmark, B.: Adaptive Control. Addison-Wesley, Reading (1989)
Shankar, S., Marc, B.: Adaptive Control: Stability, Convergence and Robustness. Prentice-Hall, New York (1989)
Krstic, M., Kanellakopoulos, I., Kokotovic, P.: Nonlinear and Adaptive Control Design. Wiley, New York (1995)
Parlitz, U., Junge, L., Kocarev, L.: Synchronization-based parameter estimation from time series. Phys. Rev. E, Stat. Nonlinear Soft Matter Phys. 54(6), 6253–6259 (1996)
Liao, T.L., Tsai, S.H.: Adaptive synchronization of chaotic systems and its application to secure communications. Chaos Solitons Fractals 11, 1387–1396 (2000)
Fradkov, A., Nijmeijer, H., Markov, A.: Adaptive Observer-based synchronisation for communication. Int. J. Bifurc. Chaos Appl. Sci. Eng. 10, 2807–2813 (2000)
Feki, M.: An adaptive chaos synchronization scheme applied to secure communication. Chaos Solitons Fractals 18, 141–148 (2003)
Chen, S.H., Lü, J.H.: Parameters identification and synchronization of chaotic systems based upon adaptive control. Phys. Lett. A 299, 353–358 (2002)
Moukam Kakmeni, F., Bowong, S., Tchawoua, C.: Nonlinear adaptive synchronization of a class of chaotic systems. Phys. Lett. A 355, 47–54 (2006)
Zhou, J., Yu, W., Li, X.: Identifying the topology of a coupled FitzHugh–Nagumo neurobiological network via a pinning mechanism. IEEE Trans. Neural Netw. 20, 1679–1684 (2009)
Liu, H., Chen, J.J., Lu, J., Cao, M.: Generalized synchronization in complex dynamical networks via adaptive couplings. Physica A 389, 1759–1770 (2010)
Guo, W., Chen, S., Sun, W.: Topology identification of the complex networks with non-delayed and delayed coupling. Phys. Lett. A 373, 3724–3729 (2009)
Xu, Y., Zhou, W., Fang, J., Lu, H.: Structure identification and adaptive synchronization of uncertain general complex dynamical networks. Phys. Lett. A 374, 272–278 (2009)
Lee, T., Liaw, D., Chen, B.: A general invariance principle for nonlinear time-varying systems and its applications. IEEE Trans. Autom. Control 46, 1989–1993 (2001)
Young, N.: An Introduction to Hilbert Space. Cambridge University Press, Cambridge (1988)
Horn, R., Johnson, C.: Matrix Analysis. Cambridge University Press, Cambridge (1986)
Slotine, J.J., Li, W.: Applied Nonlinear Control. Prentice-Hall, New York (1991)
Peng, H., Li, L., Yang, Y., Sun, F.: Conditions of parameter identification from time series. Phys. Rev. E, Stat. Nonlinear Soft Matter Phys. 83, 036202 (2011)
Yu, D.: Estimating the topology of complex dynamical networks by steady state control: generality and limitation. Automatica 46, 2035–2040 (2010)
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Sun, F., Peng, H., Xiao, J. et al. Identifying topology of synchronous networks by analyzing their transient processes. Nonlinear Dyn 67, 1457–1466 (2012). https://doi.org/10.1007/s11071-011-0081-8
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DOI: https://doi.org/10.1007/s11071-011-0081-8