Identification time-delayed fractional order chaos with functional extrema model via differential evolution

Expert Systems with Applications

Volumn 41, Issue 4 PART 2, 2014, Pages 1601-1608

  Gao, Fei ^a   Lee, Xue Jing ^a   Fei, Feng Xia ^a   Tong, Heng Qing ^a   Deng, Yan Fang ^a   Zhao, Hua Ling ^a  

^a WUHAN UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

Differential evolution algorithm; Functional extrema model; Identification time delayed fractional chaos; Nonlinear optimization; Systematic parameters and fractional orders; Unknown time delays

Indexed keywords

DIFFERENTIAL EVOLUTION; DIFFERENTIAL EVOLUTION ALGORITHMS; FRACTIONAL ORDER; FRACTIONAL-ORDER CHAOTIC SYSTEMS; INDEPENDENT VARIABLES; NON-LINEAR OPTIMIZATION; OPTIMAL COMBINATION; SYSTEMATIC PARAMETERS AND FRACTIONAL-ORDERS;

CHAOTIC SYSTEMS; EVOLUTIONARY ALGORITHMS; IDENTIFICATION (CONTROL SYSTEMS);

TIME DELAY;

EID: 84888377702     PISSN: 09574174     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.eswa.2013.08.057     Document Type: Article

References (65)

1. S.K. Agrawal, M. Srivastava, and S. Das Synchronization of fractional order chaotic systems using active control method Chaos, Solitons & Fractals 45 6 2012 737 752
2. R.L. Bagley, and R.A. Calico Fractional order state equations for the control of viscoelastically damped structures Journal of Guidance, Control, and Dynamics 14 2 1991 304 311
3. S. Bhalekar, and V. Daftardar-Gejji Fractional ordered Liu system with time-delay Communications in Nonlinear Science and Numerical Simulation 15 8 2010 2178 2191
4. S. Bhalekar, and V. Daftardar-Gejji Synchronization of different fractional order chaotic systems using active control Communications in Nonlinear Science and Numerical Simulation 15 11 2010 3536 3546
5. S. Bhalekar, and V. Daftardar-Gejji A predictor-corrector scheme for solving nonlinear delay differential equations of fractional order Journal of Fractional Calculus and Applications 1 5 2011 1 8
6. S. Bhalekar, and V. Daftardar-Gejji A predictor-corrector scheme for solving nonlinear delay differential equations of fractional order Journal of Fractional Calculus and Applications, An International Journal 1 5 2011 1 9
7. R. Caponetto, and S. Fazzino A semi-analytical method for the computation of the Lyapunov exponents of fractional-order systems Communications in Nonlinear Science and Numerical Simulation 18 1 2013 22 27
8. V. Celik, and Y. Demir Chaotic fractional order delayed cellular neural network 2010 Springer Netherlands (Ch. 27)
9. V. Celik, and Y. Demir Chaotic dynamics of the fractional order nonlinear system with time delay Signal, Image and Video Processing 2013 1 6
10. W.-D. Chang Parameter identification of Chen and Lu systems: A differential evolution approach Chaos, Solitons & Fractals 32 4 2007 1469 1476 (Pubitemid 44909760)
11. C.-W. Chiang, W.-P. Lee, and J.-S. Heh A 2-opt based differential evolution for global optimization Applied Soft Computing 10 4 2010 1200 1207
12. V. Daftardar-Gejji, S. Bhalekar, and P. Gade Dynamics of fractional-ordered Chen system with delay Pramana 79 1 2012 61 69
13. Deng, W., Sun, S. E. D., Wang, P., Zhang, D., Xu, W. 2006. Fabrication of vertical coupled polymer microring resonator. In Y.-C. Chung, S. Xie (Eds.), ICO20: Optical communication. Vol. 6025 of proceedings of the SPIE (pp. 334-339).
14. W.H. Deng, and C.P. Li Chaos synchronization of the fractional lü system Physica A: Statistical Mechanics and its Applications 353 0 2005 61 72
15. K. Diethelm An efficient parallel algorithm for the numerical solution of fractional differential equations Fractional Calculus and Applied Analysis 14 3 2011 475 490
16. K. Diethelm, N. Ford, and A. Freed A predictor-corrector approach for the numerical solution of fractional differential equations Nonlinear Dynamics 29 1-4 2002 3 22 (Pubitemid 34945390)
17. E.H. Doha, A.H. Bhrawy, and S.S. Ezz-Eldien A new Jacobi operational matrix: An application for solving fractional differential equations Applied Mathematical Modelling 36 10 2012 4931 4943
18. Fei, G., Feng-xia, F., Qian, X., Yan-fang, D., Q. Yi-bo, I. Balasingham, Reconstruction mechanism with self-growing equations for hyper, improper and proper fractional chaotic systems through a novel non-Lyapunov approach, arXiv:1207.7357.
19. F. Gao ,Fei, F.-x.Computing unstable period orbits of discrete chaotic system though differential evolutionary algorithms basing on elite subspace Xitong Gongcheng Lilun yu Shijian/System Engineering Theory and Practice 25 2005 96 102 (Pubitemid 40668784)
20. Gao, F., Fei, F.-x., Xu, Q., Deng, Y.-f., Qi, Y.-b. Identification of unknown parameters and orders via cuckoo search oriented statistically by differential evolution for non-commensurate fractional order chaotic systems. eprint arXiv:1208.0049.
21. F. Gao, F.-x. Fei, Y.-f. Deng, Y.-b. Qi, and B. Ilangko A novel non-Lyapunov approach through artificial bee colony algorithm for detecting unstable periodic orbits with high orders Expert Systems with Applications 39 16 2012 12389 12397
22. F. Gao, H. Gao, Z. Li, H. Tong, and J.-J. Lee Detecting unstable periodic orbits of nonlinear mappings by a novel quantum-behaved particle swarm optimization non-Lyapunov way Chaos, Solitons & Fractals 42 4 2009 2450 2463
23. F. Gao, X.-j. Lee, F.-x. Fei, H.-q. Tong, Y.-b. Qi, and Y.-f. Deng Parameter identification for Van Der Pol-Duffing oscillator by a novel artificial bee colony algorithm with differential evolution operators Applied Mathematics and Computation 222 0 2013 132 144
24. F. Gao, J.-J. Lee, Z. Li, H. Tong, and X. Lü Parameter estimation for chaotic system with initial random noises by particle swarm optimization Chaos, Solitons & Fractals 42 2 2009 1286 1291
25. F. Gao, Z.-Q. Li, and H.-Q. Tong Parameters estimation online for lorenz system by a novel quantum-behaved particle swarm optimization Chinese Physics B 17 4 2008 1196 1201 (Pubitemid 351571754)
26. F. Gao, Y. Qi, I. Balasingham, Q. Yin, and H. Gao A novel non-Lyapunov way for detecting uncertain parameters of chaos system with random noises Expert Systems with Applications 39 2 2012 1779 1783
27. F. Gao, Y. Qi, Q. Yin, and J. Xiao An novel optimal pid tuning and on-line tuning based on artificial bee colony algorithm The 2010 international conference on computational intelligence and software engineering (CiSE 2010) 2010 IEEE Wuhan, China 425 428
28. F. Gao, Y. Qi, Q. Yin, and J. Xiao Online synchronization of uncertain chaotic systems by artificial bee colony algorithm in a non-Lyapunov way The 2010 international conference on computational intelligence and software engineering (CiSE 2010) 2010 IEEE Wuhan, China 1 4
29. F. Gao, Y. Qi, Q. Yin, and J. Xiao An artificial bee colony algorithm for unknown parameters and time-delays identification of chaotic systems The fifth international conference on computer sciences and convergence information technology (ICCIT10) 2010 IEEE Seoul, Korea 659 664
30. F. Gao, Y. Qi, Q. Yin, and J. Xiao A novel non-Lyapunov approach in discrete chaos system with rational fraction control by artificial bee colony algorithm 2010 international conference on progress in informatics and computing(PIC-2010) 2010 IEEE Shanghai, China 317 320
31. F. Gao, Y. Qi, Q. Yin, and J. Xiao Solving problems in chaos control though an differential evolution algorithm with region zooming Applied Mechanics and Materials 110-116 2012 5048 5056
32. F. Gao, and H. Tong Computing two linchpins of topological degree by a novel differential evolution algorithm International Journal of Computational Intelligence and Applications 5 3 2005 335 350
33. F. Gao, and H.Q. Tong Parameter estimation for chaotic system based on particle swarm optimization Acta Physica Sinica 55 2 2006 577 582 (Pubitemid 43322814)
34. I. Grigorenko, and E. Grigorenko Chaotic dynamics of the fractional lorenz system Physical Review Letters 91 2003 034101-1 034101-4
35. H. Jian-Bing, X. Jian, and D. Ling-Dong Synchronizing improper fractional Chen chaotic system Journal of Shanghai University (Natural Science Edition) 17 6 2011 734 739
36. E. Kaslik, and S. Sivasundaram Analytical and numerical methods for the stability analysis of linear fractional delay differential equations Journal of Computational and Applied Mathematics 236 16 2012 4027 4041
37. P. Kenneth, M.S. Rainer, and A.L. Jouni Differential evolution: A practical approach to global optimization Natural computing series 2005 Springer-Verlag New York, Inc.
38. A.A. Kilbas, H.M. Srivastava, and J.J. Trujillo Theory and applications of fractional differential equations Volume 204 of North-Holland mathematics studies 2006 Elsevier North-Holland, Amsterdam, Netherlands
39. H. Kober On fractional integrals and derivatives The Quarterly Journal of Mathematics os-11 1 1940 193 211
40. C. Li, and G. Peng Chaos in Chen's system with a fractional order Chaos, Solitons & Fractals 22 2 2004 443 450
41. L. Li, Y. Yang, H. Peng, and X. Wang Parameters identification of chaotic systems via chaotic ant swarm Chaos, Solitons & Fractals 28 5 2006 1204 1211 (Pubitemid 41815092)
42. Z. Odibat A note on phase synchronization in coupled chaotic fractional order systems Nonlinear Analysis: Real World Applications 13 2 2012 779 789
43. Z.M. Odibat, N. Corson, M.A. Aziz-Alaoui, and C. Bertelle Synchronization of chaotic fractional-order systems via linear control International Journal of Bifurcation and Chaos 20 1 2010 81 97
44. Z.M. Odibat, N. Corson, M.A. Aziz-Alaoui, and C. Bertelle Synchronization of chaotic fractional-order systems via linear control International Journal of Bifurcation and Chaos 20 01 2010 81 97
45. U. Parlitz Estimating model parameters from time series by autosynchronization Physical Review Letters 76 8 1996 1232
46. I. Petráš Fractional-order chaotic systems Vol. 0 of nonlinear physical science 2011 Springer Berlin, Heidelberg 103 184
47. I. Petráš Fractional calculus Vol. 0 of nonlinear physical science 2011 Springer Berlin, Heidelberg 7 42
48. S. Samko, A. Kilbas, and O. Marichev Fractional integrals and derivatives: Theory and applications 1993 CRC
49. G. Si, Z. Sun, H. Zhang, and Y. Zhang Parameter estimation and topology identification of uncertain fractional order complex networks Communications in Nonlinear Science and Numerical Simulation 17 12 2012 5158 5171
50. G. Si, Z. Sun, Y. Zhang, and W. Chen Projective synchronization of different fractional-order chaotic systems with non-identical orders Nonlinear Analysis: Real World Applications 13 4 2012 1761 1771
51. L. Song, J. Yang, and S. Xu Chaos synchronization for a class of nonlinear oscillators with fractional order Nonlinear Analysis: Theory, Methods and Applications 72 5 2010 2326 2336
52. R. Storn, and K. Price Differential evolution & ndash; a simple and efficient heuristic for global optimization over continuous spaces Journal of Global Optimization 11 4 1997 341 359 (Pubitemid 127502202)
53. Z. Sun, G. Si, F. Min, and Y. Zhang Adaptive modified function projective synchronization and parameter identification of uncertain hyperchaotic (chaotic) systems with identical or non-identical structures Nonlinear Dynamics 68 4 2012 471 486
54. N.H. Sweilam, M.M. Khader, and A.M.S. Mahdy Numerical studies for fractional-order logistic differential equation with two different delays Journal of Applied Mathematics 2012 2012 14
55. Y. Tang, X. Zhang, C. Hua, L. Li, and Y. Yang Parameter identification of commensurate fractional-order chaotic system via differential evolution Physics Letters A 376 4 2012 457 464
56. M.S. Tavazoei, and M. Haeri A necessary condition for double scroll attractor existence in fractional-order systems Physics Letters A 367 1 2007 102 113
57. M.S. Tavazoei, and M. Haeri Chaotic attractors in incommensurate fractional order systems Physica D: Nonlinear Phenomena 237 20 2008 2628 2637
58. X. Wang, X. Zhang, and C. Ma Modified projective synchronization of fractional-order chaotic systems via active sliding mode control Nonlinear Dynamics 69 1-2 2012 511 517
59. X. Wu, D. Lai, and H. Lu Generalized synchronization of the fractional-order chaos in weighted complex dynamical networks with nonidentical nodes Nonlinear Dynamics 69 1-2 2012 667 683 (export Date: 27 June 2012 Source: Scopus)
60. X.J. Wu, and S.L. Shen Chaos in the fractional-order lorenz system International Journal of Computer Mathematics 86 7 2009 1274 1282 (cited By (since 1996): 5 Export Date: 27 June 2012 Source: Scopus)
61. X. Wu, Z. Sun, F. Liang, and C. Yu Online estimation of unknown delays and parameters in uncertain time delayed dynamical complex networks via adaptive observer Nonlinear Dynamics 73 3 2013 1753 1768
62. K. Yang, K. Maginu, and H. Nomura Parameters identification of chaotic systems by quantum-behaved particle swarm optimization International Journal of Computer Mathematics 86 12 2009 2225 2235
63. L.-G. Yuan, and Q.-G. Yang Parameter identification and synchronization of fractional-order chaotic systems Communications in Nonlinear Science and Numerical Simulation 17 1 2012 305 316
64. L. Yuan, Q. Yang, and C. Zeng Chaos detection and parameter identification in fractional-order chaotic systems with delay Nonlinear Dynamics 73 1-2 2013 439 448
65. R.X. Zhang, Y. Yang, and S.P. Yang Adaptive synchronization of the fractional-order unified chaotic system Wuli Xuebao/Acta Physica Sinica 58 9 2009 6039 6044