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Volumn 57, Issue 3, 2009, Pages 363-373

Describing function based methods for predicting chaos in a class of fractional order differential equations

Author keywords

Chaos; Describing function; Fractional order differential equation

Indexed keywords

CHAOS; CHAOTIC DYNAMICS; CUBIC NONLINEARITIES; DESCRIBING FUNCTION METHODS; FRACTIONAL ORDER; FRACTIONAL ORDER DIFFERENTIAL EQUATION; INTEGER ORDER; NUMERICAL SIMULATION;

EID: 68249152474     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-008-9447-y     Document Type: Article
Times cited : (35)

References (49)
  • 1
    • 84956246670 scopus 로고
    • Dead matter has memory!
    • S. Westerlund 1991 Dead matter has memory! Phys. Scr. 43 2 174 179
    • (1991) Phys. Scr. , vol.43 , Issue.2 , pp. 174-179
    • Westerlund, S.1
  • 2
    • 0026124343 scopus 로고
    • Fractional order state equations for the control of visco-elastically damped structures
    • R.L. Bagley R.A. Calico 1991 Fractional order state equations for the control of visco-elastically damped structures J. Guid. Control and Dyn. 14 304 311
    • (1991) J. Guid. Control and Dyn. , vol.14 , pp. 304-311
    • Bagley, R.L.1    Calico, R.A.2
  • 3
    • 0030736195 scopus 로고    scopus 로고
    • Application of fractional derivatives to the analysis of damped vibrations of viscoelastic single mass system
    • Y.A. Rossikhin M.V. Shitikova 1997 Application of fractional derivatives to the analysis of damped vibrations of viscoelastic single mass system Acta Mech. 120 109 125
    • (1997) Acta Mech. , vol.120 , pp. 109-125
    • Rossikhin, Y.A.1    Shitikova, M.V.2
  • 4
    • 0030127310 scopus 로고    scopus 로고
    • On fractional calculus and fractional multipoles in electromagnetism
    • N. Engheta 1996 On fractional calculus and fractional multipoles in electromagnetism IEEE Trans. Antennas Propag. 44 4 554 566
    • (1996) IEEE Trans. Antennas Propag. , vol.44 , Issue.4 , pp. 554-566
    • Engheta, N.1
  • 8
    • 33745712064 scopus 로고    scopus 로고
    • Fractional-order control strategies for power electronic buck converters
    • A.J. Calderon B.M. Vinagre V. Feliu-Batlle 2006 Fractional-order control strategies for power electronic buck converters Signal Process. 86 2803 2819
    • (2006) Signal Process , vol.86 , pp. 2803-2819
    • Calderon, A.J.1    Vinagre, B.M.2    Feliu-Batlle, V.3
  • 9
    • 33847623276 scopus 로고    scopus 로고
    • Fractional robust control of main irrigation canals with variable dynamic parameters
    • V. Feliu-Batlle R. Rivas Perez L. Sanchez Rodriguez 2007 Fractional robust control of main irrigation canals with variable dynamic parameters Control Eng. Pract. 15 673 686
    • (2007) Control Eng. Pract. , vol.15 , pp. 673-686
    • Feliu-Batlle, V.1    Rivas Perez, R.2    Sanchez Rodriguez, L.3
  • 10
    • 45949102670 scopus 로고    scopus 로고
    • Fractional controller to stabilize fixed points of uncertain chaotic systems: Theoretical and experimental study
    • M.S. Tavazoei M. Haeri S. Jafari 2008 Fractional controller to stabilize fixed points of uncertain chaotic systems: Theoretical and experimental study J. Syst. Control Eng. Part I 222 175 184
    • (2008) J. Syst. Control Eng. Part i , vol.222 , pp. 175-184
    • Tavazoei, M.S.1    Haeri, M.2    Jafari, S.3
  • 11
    • 33847067879 scopus 로고    scopus 로고
    • Does the fractional Brusselator with efficient dimension less than 1 have a limit cycle?
    • Y. Wang C. Li 2007 Does the fractional Brusselator with efficient dimension less than 1 have a limit cycle? Phys. Lett. A 363 414 419
    • (2007) Phys. Lett. A , vol.363 , pp. 414-419
    • Wang, Y.1    Li, C.2
  • 12
    • 34748856163 scopus 로고    scopus 로고
    • Analysis of the Van der Pol oscillator containing derivatives of fractional order
    • R.S. Barbosa J.A.T. Machado B.M. Vingare A.J. Calderon 2007 Analysis of the Van der Pol oscillator containing derivatives of fractional order J. Vib. Control 13 9-10 1291 1301
    • (2007) J. Vib. Control , vol.13 , Issue.9-10 , pp. 1291-1301
    • Barbosa, R.S.1    MacHado, J.A.T.2    Vingare, B.M.3    Calderon, A.J.4
  • 13
  • 14
    • 52549089142 scopus 로고    scopus 로고
    • Regular oscillations or chaos in a fractional order system with any effective dimension
    • M.S. Tavazoei M. Haeri 2008 Regular oscillations or chaos in a fractional order system with any effective dimension Nonlinear Dyn. 54 3 213 222
    • (2008) Nonlinear Dyn. , vol.54 , Issue.3 , pp. 213-222
    • Tavazoei, M.S.1    Haeri, M.2
  • 16
    • 33846056956 scopus 로고    scopus 로고
    • Design of multidirectional multiscroll chaotic attractors based on fractional differential systems via switching control
    • W. Deng J. Lü 2006 Design of multidirectional multiscroll chaotic attractors based on fractional differential systems via switching control Chaos 16 043120
    • (2006) Chaos , vol.16 , pp. 043120
    • Deng, W.1    Lü, J.2
  • 17
    • 34347330038 scopus 로고    scopus 로고
    • A necessary condition for double scroll attractor existence in fractional order systems
    • M.S. Tavazoei M. Haeri 2007 A necessary condition for double scroll attractor existence in fractional order systems Phys. Lett. A 367 1-2 102 113
    • (2007) Phys. Lett. A , vol.367 , Issue.1-2 , pp. 102-113
    • Tavazoei, M.S.1    Haeri, M.2
  • 18
    • 1442346520 scopus 로고    scopus 로고
    • Chaotic behavior in noninteger-order cellular neural networks
    • P. Arena L. Fortuna D. Porto 2000 Chaotic behavior in noninteger-order cellular neural networks Phys. Rev. E 61 1 776 781
    • (2000) Phys. Rev. e , vol.61 , Issue.1 , pp. 776-781
    • Arena, P.1    Fortuna, L.2    Porto, D.3
  • 19
    • 13844266555 scopus 로고    scopus 로고
    • A nonlinear differential equation of fractional order with chaotic properties
    • M. Seredynska A. Hanyga 2004 A nonlinear differential equation of fractional order with chaotic properties Int. J. Bifurc. Chaos 14 4 1291 1304
    • (2004) Int. J. Bifurc. Chaos , vol.14 , Issue.4 , pp. 1291-1304
    • Seredynska, M.1    Hanyga, A.2
  • 20
    • 33746617393 scopus 로고    scopus 로고
    • Analysing chaos in fractional-order systems with the harmonic balance method
    • Z.M. Wu J.G. Lu J.Y. Xie 2006 Analysing chaos in fractional-order systems with the harmonic balance method Chin. Phys. 15 6 1201 1207
    • (2006) Chin. Phys. , vol.15 , Issue.6 , pp. 1201-1207
    • Wu, Z.M.1    Lu, J.G.2    Xie, J.Y.3
  • 21
    • 1842832060 scopus 로고    scopus 로고
    • Chaos in Chen's system with a fractional order
    • C.P. Li G.J. Peng 2004 Chaos in Chen's system with a fractional order Chaos Solitons Fractals 22 2 443 450
    • (2004) Chaos Solitons Fractals , vol.22 , Issue.2 , pp. 443-450
    • Li, C.P.1    Peng, G.J.2
  • 22
    • 33846202580 scopus 로고    scopus 로고
    • Scaling attractors of fractional differential systems
    • C.P. Li W.H. Deng G. Chen 2006 Scaling attractors of fractional differential systems Fractals 14 4 303 314
    • (2006) Fractals , vol.14 , Issue.4 , pp. 303-314
    • Li, C.P.1    Deng, W.H.2    Chen, G.3
  • 23
    • 33645166246 scopus 로고    scopus 로고
    • Chaos synchronization of fractional-order differential system
    • C.P. Li W.H. Deng 2006 Chaos synchronization of fractional-order differential system Int. J. Mod. Phys. B 20 7 791 803
    • (2006) Int. J. Mod. Phys. B , vol.20 , Issue.7 , pp. 791-803
    • Li, C.P.1    Deng, W.H.2
  • 24
    • 34247866598 scopus 로고    scopus 로고
    • Generalized synchronization in fractional order systems
    • W.H. Deng 2007 Generalized synchronization in fractional order systems Phys. Rev. E 75 0565201-1 0565201-7
    • (2007) Phys. Rev. e , vol.75 , pp. 05652011-05652017
    • Deng, W.H.1
  • 25
    • 0038045559 scopus 로고    scopus 로고
    • No-chaos criteria for certain classes of driven nonlinear oscillators
    • S.J. Linz 2003 No-chaos criteria for certain classes of driven nonlinear oscillators Acta Phys. Pol. B 34 7 3741 3749
    • (2003) Acta Phys. Pol. B , vol.34 , Issue.7 , pp. 3741-3749
    • Linz, S.J.1
  • 27
  • 28
    • 51249088596 scopus 로고    scopus 로고
    • Chaotic attractors in incommensurate fractional order systems
    • M.S. Tavazoei M. Haeri 2008 Chaotic attractors in incommensurate fractional order systems Physica D 237 20 2628 2637
    • (2008) Physica D , vol.237 , Issue.20 , pp. 2628-2637
    • Tavazoei, M.S.1    Haeri, M.2
  • 30
    • 0036650479 scopus 로고    scopus 로고
    • A predictor-corrector approach for the numerical solution of fractional differential equations
    • K. Diethelm N.J. Ford A.D. Freed 2002 A predictor-corrector approach for the numerical solution of fractional differential equations Nonlinear Dyn. 29 3 22
    • (2002) Nonlinear Dyn. , vol.29 , pp. 3-22
    • Diethelm, K.1    Ford, N.J.2    Freed, A.D.3
  • 31
    • 3042709180 scopus 로고    scopus 로고
    • Multi-order fractional differential equations and their numerical solution
    • D. Diethelm N.J. Ford 2004 Multi-order fractional differential equations and their numerical solution Appl. Math. Comput. 154 3 621 640
    • (2004) Appl. Math. Comput. , vol.154 , Issue.3 , pp. 621-640
    • Diethelm, D.1    Ford, N.J.2
  • 32
    • 34247212711 scopus 로고    scopus 로고
    • Remarks on fractional derivatives
    • C. Li W. Deng 2007 Remarks on fractional derivatives Appl. Math. Comput. 187 777 784
    • (2007) Appl. Math. Comput. , vol.187 , pp. 777-784
    • Li, C.1    Deng, W.2
  • 33
    • 0002339320 scopus 로고    scopus 로고
    • The effects of continuously varying the fractional differential order of a chaotic nonlinear system
    • S. Nimmo A.K. Evans 1999 The effects of continuously varying the fractional differential order of a chaotic nonlinear system Chaos Solitons Fractals 10 1111 1118
    • (1999) Chaos Solitons Fractals , vol.10 , pp. 1111-1118
    • Nimmo, S.1    Evans, A.K.2
  • 34
    • 34249335010 scopus 로고    scopus 로고
    • Short memory principle and a predictor-corrector approach for fractional differential equations
    • W.H. Deng 2007 Short memory principle and a predictor-corrector approach for fractional differential equations J. Comput. Appl. Math. 206 1 174 188
    • (2007) J. Comput. Appl. Math. , vol.206 , Issue.1 , pp. 174-188
    • Deng, W.H.1
  • 35
    • 36149001762 scopus 로고    scopus 로고
    • Numerical algorithm for the time fractional Fokker-Planck equation
    • W.H. Deng 2007 Numerical algorithm for the time fractional Fokker-Planck equation J. Comput. Phys. 227 1510 1522
    • (2007) J. Comput. Phys. , vol.227 , pp. 1510-1522
    • Deng, W.H.1
  • 36
    • 37549042003 scopus 로고    scopus 로고
    • Unreliability of frequency-domain approximation in recognizing chaos in fractional-order systems
    • M.S. Tavazoei M. Haeri 2007 Unreliability of frequency-domain approximation in recognizing chaos in fractional-order systems IET Signal Process. 1 4 171 181
    • (2007) IET Signal Process , vol.1 , Issue.4 , pp. 171-181
    • Tavazoei, M.S.1    Haeri, M.2
  • 38
    • 0001110962 scopus 로고    scopus 로고
    • Coprime factorizations and stability of fractional differential systems
    • C. Bonnet J.R. Partington 2000 Coprime factorizations and stability of fractional differential systems Syst. Control Lett. 41 167 174
    • (2000) Syst. Control Lett. , vol.41 , pp. 167-174
    • Bonnet, C.1    Partington, J.R.2
  • 39
    • 56349146591 scopus 로고    scopus 로고
    • Some applications of fractional calculus in suppression of chaotic oscillations
    • M.S. Tavazoei M. Haeri S. Jafari S. Bolouki M. Siami 2008 Some applications of fractional calculus in suppression of chaotic oscillations IEEE Trans. Ind. Electron. 55 11 4094 4101
    • (2008) IEEE Trans. Ind. Electron. , vol.55 , Issue.11 , pp. 4094-4101
    • Tavazoei, M.S.1    Haeri, M.2    Jafari, S.3    Bolouki, S.4    Siami, M.5
  • 40
    • 0026189557 scopus 로고
    • Chaos prediction in nonlinear feedback systems
    • R. Genesio A. Tesi 1991 Chaos prediction in nonlinear feedback systems IEE Proc. D 138 313 320
    • (1991) IEE Proc. D , vol.138 , pp. 313-320
    • Genesio, R.1    Tesi, A.2
  • 41
    • 0026866475 scopus 로고
    • Harmonic balance methods for the analysis of chaotic dynamics in nonlinear systems
    • R. Genesio A. Tesi 1992 Harmonic balance methods for the analysis of chaotic dynamics in nonlinear systems Automatica 28 3 531 548
    • (1992) Automatica , vol.28 , Issue.3 , pp. 531-548
    • Genesio, R.1    Tesi, A.2
  • 42
    • 0002456064 scopus 로고
    • A harmonic balance approach for chaos prediction: Chua's Circuit
    • R. Genesio A. Tesi 1992 A harmonic balance approach for chaos prediction: Chua's Circuit Int. J. Bifurc. Chaos 2 1 61 79
    • (1992) Int. J. Bifurc. Chaos , vol.2 , Issue.1 , pp. 61-79
    • Genesio, R.1    Tesi, A.2
  • 43
    • 0027699599 scopus 로고
    • A frequency approach for analyzing and controlling chaos in nonlinear circuits
    • R. Genesio A. Tesi F. Villoresi 1993 A frequency approach for analyzing and controlling chaos in nonlinear circuits IEEE Trans. Circuits Syst. I 40 11 819 828
    • (1993) IEEE Trans. Circuits Syst. i , vol.40 , Issue.11 , pp. 819-828
    • Genesio, R.1    Tesi, A.2    Villoresi, F.3
  • 44
    • 33750550632 scopus 로고    scopus 로고
    • Harmonic balance analysis of the generalized Chua's circuit
    • F.A. Savaci S. Gunel 2006 Harmonic balance analysis of the generalized Chua's circuit Int. J. Bifurc. Chaos 16 8 2325 2332
    • (2006) Int. J. Bifurc. Chaos , vol.16 , Issue.8 , pp. 2325-2332
    • Savaci, F.A.1    Gunel, S.2
  • 46
    • 3042916490 scopus 로고
    • Limit cycle stability
    • A.I. Mees 1973 Limit cycle stability IMA J. Appl. Math. 11 3 281 295
    • (1973) IMA J. Appl. Math. , vol.11 , Issue.3 , pp. 281-295
    • Mees, A.I.1
  • 47
    • 0033078110 scopus 로고    scopus 로고
    • A simple criterion for the occurrence of chaos in nonlinear feedback systems
    • K. Hirai 1999 A simple criterion for the occurrence of chaos in nonlinear feedback systems Electron. Commun. Jpn. Part 3 82 2 11 19
    • (1999) Electron. Commun. Jpn. Part 3 , vol.82 , Issue.2 , pp. 11-19
    • Hirai, K.1
  • 49
    • 68249161560 scopus 로고    scopus 로고
    • Analysis of bifurcation and chaos by describing function method
    • Hirai, K.: Analysis of bifurcation and chaos by describing function method. Chaos Memorial Symposium in Asuka, pp. 13-18 (1997)
    • (1997) Chaos Memorial Symposium in Asuka , pp. 13-18
    • Hirai, K.1


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