Parameter estimation and topology identification of uncertain fractional order complex networks

Communications in Nonlinear Science and Numerical Simulation

Volumn 17, Issue 12, 2012, Pages 5158-5171

  Si, Gangquan ^a   Sun, Zhiyong ^a   Zhang, Hongying ^a   Zhang, Yanbin ^a  

^a XI'AN JIAOTONG UNIVERSITY   (China)

Author keywords

Adaptive synchronization; Fractional calculus; Fractional order complex network; Network identification

Indexed keywords

ADAPTIVE CONTROL SYSTEMS; CALCULATIONS; NETWORK TOPOLOGY; PARAMETER ESTIMATION; UNCERTAINTY ANALYSIS;

ADAPTIVE SYNCHRONIZATIONS; FRACTIONAL CALCULUS; FRACTIONAL ORDER; FRACTIONAL ORDER COMPLEX NETWORK; IDENTIFICATION PROBLEM; NETWORK IDENTIFICATION; NETWORK TOPOLOGY; PARAMETERS ESTIMATION; SYSTEMS NETWORKS; TOPOLOGY IDENTIFICATION;

COMPLEX NETWORKS;

EID: 84864407494     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2012.05.005     Document Type: Article

References (52)

1. Strogatz S.H. Exploring complex networks. Nature 2001, 410:268-276.
2. Wang X.F., Chen G. Complex networks: small-world, scale-free and beyond. Circuits Syst Mag IEEE 2003, 3:6-20.
3. Boccaletti S., Latora V., Moreno Y., Chavez M., Hwang D.U. Complex networks: structure and dynamics. Phys Rep 2006, 424:175-308.
4. Albert R., Barabasi A.L. Statistical mechanics of complex networks. Rev Mod Phys 2002, 74:47.
5. Yang S.J. Exploring complex networks by walking on them. Phys Rev E 2005, 71:016107.
6. Wang X.F., Chen G. Pinning control of scale-free dynamical networks. Physica A 2002, 310:521-531.
7. Cao J., Lu J. Adaptive synchronization of neural networks with or without time-varying delay. Chaos 2006, 16:013133.
8. Yu W.W., Chen G.R., Lü J.H. On pinning synchronization of complex dynamical networks. Automatica 2009, 45:429-435.
9. Chen S.Q., Chen B. Defining indirect uncertainty in system-based risk management. Ecol Inf 2011, 10.1016/j.ecoinf.2011.05.005.
10. Liu H., Lu J.A., Lü J.H., Hill D.J. Structure identification of uncertain general complex dynamical networks with time delay. Automatica 2009, 45:1799-1807.
11. Parlitz U. Estimating model parameters from time series by autosynchronization. Phys Rev Lett 1996, 76:1232-1235.
12. Konnur R. Synchronization-based approach for estimating all model parameters of chaotic systems. Phys Rev E 2003, 67:027204.
13. Huang D. Synchronization-based estimation of all parameters of chaotic systems from time series. Phys Rev E 2004, 69:067201.
14. Yu W.W., Chen G.R., Cao J.D., Lü J.H., Parlitz U. Parameter identification of dynamical systems from time series. Phys Rev E 2007, 75:067201.
15. Peng H., Li L., Yang Y., Sun F. Conditions of parameter identification from time series. Phys Rev E 2011, 83:036202.
16. Yu D., Righero M., Kocarev L. Estimating topology of networks. Phys Rev Lett 2006, 97:188701.
17. Zhou J., Lu J. Topology identification of weighted complex dynamical networks. Physica A 2007, 386:481-491.
18. Wu X. Synchronization-based topology identification of weighted general complex dynamical networks with time-varying coupling delay. Physica A 2008, 387:997-1008.
19. Mainardi F. Fractional relaxation-oscillation and fractional diffusion-wave phenomena. Chaos Solitons Fractals 1996, 7:1461-1477.
20. Zaslavsky G.M. Chaos, fractional kinetics, and anomalous transport. Phys Rep 2002, 371:461-580.
21. Mainardi F. Fractional calculus and waves in linear viscoelasticity: an introduction to mathematical models 2009, Imperial College Press, London.
22. Bai J., Yu Y., Wang S., Song Y. Modified projective synchronization of uncertain fractional order hyperchaotic systems. Commun Nonlinear Sci Numer Simul 2012, 17:1921-1928.
23. Moaddy K., Hashim I., Momani S. Non-standard finite difference schemes for solving fractional-order Rössler chaotic and hyperchaotic systems. Comput Math Appl 2011, 62:1068-1074.
24. Tang Y., Wang Z., Fang J. Pinning control of fractional-order weighted complex networks. Chaos 2009, 19:013112.
25. Tang Y., Fang J. Synchronization of N-coupled fractional-order chaotic systems with ring connection. Commun Nonlinear Sci Numer Simul 2010, 15:401-412.
26. Wang J., Zhang Y. Network synchronization in a population of star-coupled fractional nonlinear oscillators. Phys Lett A 2010, 374:1464-1468.
27. Wu X.J., Lu H.T. Outer synchronization between two different fractional-order general complex dynamical networks. Chin Phys B 2010, 19:070511.
28. Asheghan M.M., Miguez J., Hamidi-Beheshti M.T., Tavazoei M.S. Robust outer synchronization between two complex networks with fractional order dynamics. Chaos 2011, 21:033121.
29. Wu X., Lai D., Lu H. Generalized synchronization of the fractional-order chaos in weighted complex dynamical networks with nonidentical nodes. Nonlinear Dyn 2012, 69:667-683.
30. Podlubny I. Fractional differential equations 1999, Academic press, New York.
31. Matignon D. Stability results for fractional differential equations with applications to control processing. In: Computational engineering in systems applications multiconference, proceeeding of IMACS, IEEE-SMC, Lille, France: 1996, pp. 963-968.
32. Hu J.B., Han Y., Zhao L.D. Synchronizing fractional chaotic systems based on Lyapunov equation. Acta Phy Sin 2008, 57:7522-7526.
33. Hu J.B., Han Y., Zhao L.D. A novel stability theorem for fractional systems and its applying in synchronizing fractional chaotic system based on back-stepping approcach. Acta Phys Sin 2009, 58:2235-2239.
34. Qin C.M., Qi N.M., Zhu K. State space modeling and stability theory of variable fractional order system (in Chinese). Control Decis 2011, 26:1757-1760.
35. Vinagre B., Podlubny I., Hernandez A., Feliu V. Some approximations of fractional order operators used in control theory and applications. Fract Calculus Appl Anal 2000, 3:231-248.
36. Aoun M., Malti R., Levron F., Oustaloup A. Numerical simulations of fractional systems: an overview of existing methods and improvements. Nonlinear Dyn 2004, 38:117-131.
37. Tavazoei M.S., Haeri M., Bolouki S., Siami M. Stability preservation analysis for frequency-based methods in numerical simulation of fractional order systems. SIAM J Numer Anal 2008, 47:321-338.
38. Diethelm K., Ford N.J., Freed A.D. A predictor-corrector approach for the numerical solution of fractional differential equations. Nonlinear Dyn 2002, 29:3-22.
39. Liao T.L., Huang N.S. An observer-based approach for chaotic synchronization with applications to secure communications. IEEE Trans Circuits Syst I 1999, 46:1144-1150.
40. Andrilli S.F., Hecker D. Elementary linear algebra 2010, Academic Press. Fourth ed.
41. Zhao J., Li Q., Lu J.A., Jiang Z.P. Topology identification of complex dynamical networks. Chaos 2010, 20:023119.
42. Xu Y., Zhou W., Fang J.a., Lu H. Structure identification and adaptive synchronization of uncertain general complex dynamical networks. Phys Lett A 2009, 374:272-278.
43. Li Y., Chen Y.Q., Podlubny I. Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag-Leffler stability. Comput Math Appl 2010, 59:1810-1821.
44. Zhang W., Tang Y., Fang J.-a., Zhu W. Exponential cluster synchronization of impulsive delayed genetic oscillators with external disturbances. Chaos 2011, 21:043137.
45. Zou W., Lu J., Tang Y., Zhang C., Kurths J. Control of delay-induced oscillation death by coupling phase in coupled oscillators. Phys Rev E 2011, 84:066208.
46. Trigeassou J.C., Maamri N., Sabatier J., Oustaloup A. A Lyapunov approach to the stability of fractional differential equations. Signal Process 2011, 91:437-445.
47. Li C., Zhang F. A survey on the stability of fractional differential equations. Eur Phys J Special Topics 2011, 193:27-47.
48. Grigorenko I., Grigorenko E. Chaotic dynamics of the fractional Lorenz system. Phys Rev Lett 2003, 91:34101.
49. Chen L., Lu J., Tse C.K. Synchronization: an obstacle to identification of network topology. IEEE Trans Circuits Syst II 2009, 56:310-314.
50. Bhalekar S., Daftardar-Gejji V. Synchronization of different fractional order chaotic systems using active control. Commun Nonlinear Sci Numer Simul 2010, 15:3536-3546.
51. Tavazoei M.S., Haeri M. Chaotic attractors in incommensurate fractional order systems. Physica D 2008, 237:2628-2637.
52. Lin W., Ma H.F. Failure of parameter identification based on adaptive synchronization techniques. Phys Rev E 2007, 75:066212.