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Volumn 2011, Issue , 2011, Pages

Chaotic incommensurate fractional order Rössler system: Active control and synchronization

Author keywords

Active control; Chaos; Fractional order system; R ssler system; Synchronization

Indexed keywords


EID: 84866915975     PISSN: 16871839     EISSN: 16871847     Source Type: Journal    
DOI: 10.1186/1687-1847-2011-15     Document Type: Article
Times cited : (61)

References (38)
  • 1
    • 0035826148 scopus 로고    scopus 로고
    • Synchronization and rhythmic processes in physiology
    • doi:10.1038/35065745
    • Glass, L: Synchronization and rhythmic processes in physiology. Nature. 410, 277-284 (2001). doi:10.1038/35065745
    • (2001) Nature , vol.410 , pp. 277-284
    • Glass, L.1
  • 2
    • 0037217052 scopus 로고    scopus 로고
    • Cancer chronotherapy: Principles, applications, and perspectives
    • Mormont, MC, Levi, F: Cancer chronotherapy: principles, applications, and perspectives. Cancer. 97, 155-169 (2002)
    • (2002) Cancer , vol.97 , pp. 155-169
    • Mormont, M.C.1    Levi, F.2
  • 6
    • 0033826176 scopus 로고    scopus 로고
    • Endogenous circadian rhythm of pulmonary function in healthy humans
    • Spengler, CM, Shea, SA: Endogenous circadian rhythm of pulmonary function in healthy humans. Am J Respir Crit Care Med. 162, 1038-1046 (2000)
    • (2000) Am J Respir Crit Care Med. , vol.162 , pp. 1038-1046
    • Spengler, C.M.1    Shea, S.A.2
  • 7
    • 0037079015 scopus 로고    scopus 로고
    • Computational approaches to cellular rhythms
    • doi:10.1038/nature01259
    • Goldbeter, A: Computational approaches to cellular rhythms. Nature. 420, 238-245 (2002). doi:10.1038/nature01259
    • (2002) Nature , vol.420 , pp. 238-245
    • Goldbeter, A.1
  • 9
    • 38149125451 scopus 로고    scopus 로고
    • Chaos control via a simple fractional order controller
    • doi:10.1016/j.physleta.2007.08.040
    • Tavazoei, MS, Haeri, M: Chaos control via a simple fractional order controller. Phys Lett A. 372, 798-807 (2008). doi:10.1016/j.physleta.2007.08.040
    • (2008) Phys Lett A , vol.372 , pp. 798-807
    • Tavazoei, M.S.1    Haeri, M.2
  • 10
    • 34249053502 scopus 로고    scopus 로고
    • Impulsive effects on stability of fuzzy Cohen-Grossberg neural networks with time-varying delays
    • Song, Q, Cao, J: Impulsive effects on stability of fuzzy Cohen-Grossberg neural networks with time-varying delays. IEEE Trans Syst Man Cybern B Cybern. 37(3), 733-741 (2007)
    • (2007) IEEE Trans Syst Man Cybern B Cybern , vol.37 , Issue.3 , pp. 733-741
    • Song, Q.1    Cao, J.2
  • 11
    • 33947172554 scopus 로고    scopus 로고
    • Adaptive lag synchronization of unknown chaotic delayed neural networks with noise perturbation
    • doi:10.1016/j.physleta.2006.12.019
    • Sun, Y, Cao, J: Adaptive lag synchronization of unknown chaotic delayed neural networks with noise perturbation. Phys Lett A. 364, 277-285 (2007). doi:10.1016/j.physleta.2006.12.019
    • (2007) Phys Lett A , vol.364 , pp. 277-285
    • Sun, Y.1    Cao, J.2
  • 13
    • 3543144649 scopus 로고    scopus 로고
    • Effect of the pyragas feedback on the dynamics of laser with modulation of losses
    • Loiko, NA, Naumenko, AV, Turovets, SI: Effect of the pyragas feedback on the dynamics of laser with modulation of losses. Zh Eksp Teor Fiz. 112(4), 1516-1530 (1997)
    • (1997) Zh Eksp Teor Fiz. , vol.112 , Issue.4 , pp. 1516-1530
    • Loiko, N.A.1    Naumenko, A.V.2    Turovets, S.I.3
  • 14
    • 0008849269 scopus 로고    scopus 로고
    • From simple to complex oscillatory behavior in metabolic and genetic control network
    • doi:10.1063/1.1345727
    • Goldbeter, A, Gonze, D, Houart, G, Leloup, JC, Halloy, J, Dupont, G: From simple to complex oscillatory behavior in metabolic and genetic control network. Chaos. 11, 247-260 (2001). doi:10.1063/1.1345727
    • (2001) Chaos , vol.11 , pp. 247-260
    • Goldbeter, A.1    Gonze, D.2    Houart, G.3    Leloup, J.C.4    Halloy, J.5    Dupont, G.6
  • 15
    • 0347126689 scopus 로고    scopus 로고
    • Theoretical models in chronotherapy: I. Periodic perturbations in oscillating chemical reactions
    • doi:10.1076/brhm.34.3.241.18813
    • Salazar, C, Garcia, L, Rodriguez, Y, Garcia, JM, Quintana, R, Rieumont, J, Nieto-Villar, JM: Theoretical models in chronotherapy: I. Periodic perturbations in oscillating chemical reactions. Biol Rhythm Res. 34, 241-249 (2003). doi:10.1076/brhm.34.3.241.18813
    • (2003) Biol Rhythm Res. , vol.34 , pp. 241-249
    • Salazar, C.1    Garcia, L.2    Rodriguez, Y.3    Garcia, J.M.4    Quintana, R.5    Rieumont, J.6    Nieto-Villar, J.M.7
  • 16
    • 0026124343 scopus 로고
    • Fractional order state equations for the control of visco-elastically damped structures
    • doi:10.2514/3.20641
    • Bagley, RL, Calico, RA: Fractional order state equations for the control of visco-elastically damped structures. J Guidance Control Dyn. 14, 304-311 (1991). doi:10.2514/3.20641
    • (1991) J Guidance Control Dyn. , vol.14 , pp. 304-311
    • Bagley, R.L.1    Calico, R.A.2
  • 17
    • 0034517069 scopus 로고    scopus 로고
    • Fractional market dynamics
    • doi:10.1016/S0378-4371(00)00387-3
    • Laskin, N: Fractional market dynamics. Physica A. 287, 482-492 (2000). doi:10.1016/S0378-4371(00)00387-3
    • (2000) Physica A , vol.287 , pp. 482-492
    • Laskin, N.1
  • 18
    • 0030127310 scopus 로고    scopus 로고
    • On fractional calculus and fractional multipoles in electromagnetism
    • doi:10.1109/8.489308
    • Engheta, N: On fractional calculus and fractional multipoles in electromagnetism. IEEE Trans Antennas Propagat. 44(4), 554-566 (1996). doi:10.1109/8.489308
    • (1996) IEEE Trans Antennas Propagat. , vol.44 , Issue.4 , pp. 554-566
    • Engheta, N.1
  • 19
    • 45949102670 scopus 로고    scopus 로고
    • Fractional controller to stabilize fixed points of uncertain chaotic systems: Theoretical and experimental study
    • Tavazoei, MS, Haeri, M, Jafari, S: Fractional controller to stabilize fixed points of uncertain chaotic systems: theoretical and experimental study. J Syst Control Eng. 222(part I), 175-184 (2008)
    • (2008) J Syst Control Eng. , vol.222 , Issue.PART I , pp. 175-184
    • Tavazoei, M.S.1    Haeri, M.2    Jafari, S.3
  • 20
    • 50049123574 scopus 로고    scopus 로고
    • Analysis of undamped oscillations generated by marginally stable fractional order systems
    • doi:10.1016/j.sigpro.2008.07.002
    • Tavazoei, MS, Haeri, M, Nazari, N: Analysis of undamped oscillations generated by marginally stable fractional order systems. Signal Process. 88, 2971-2978 (2008). doi:10.1016/j.sigpro.2008.07.002
    • (2008) Signal Process , vol.88 , pp. 2971-2978
    • Tavazoei, M.S.1    Haeri, M.2    Nazari, N.3
  • 21
    • 0030216463 scopus 로고    scopus 로고
    • The CRONE suspension
    • doi:10.1016/0967-0661(96)00109-8
    • Oustaloup, A, Moreau, X, Nouillant, M: The CRONE suspension. Control Eng Pract. 4(8), 1101-1108 (1996). doi:10.1016/0967-0661(96)00109-8
    • (1996) Control Eng Pract. , vol.4 , Issue.8 , pp. 1101-1108
    • Oustaloup, A.1    Moreau, X.2    Nouillant, M.3
  • 22
    • 36749047507 scopus 로고    scopus 로고
    • The synchronization of fractional-order Rössler hyperchaotic systems
    • doi:10.1016/j.physa.2007.10.052
    • Yu, Y, Li, HX: The synchronization of fractional-order Rössler hyperchaotic systems. Physica A Stat Mech Appl. 387(5-6), 1393-1403 (2008). doi:10.1016/j.physa.2007.10.052
    • (2008) Physica a Stat Mech Appl. , vol.387 , Issue.5-6 , pp. 1393-1403
    • Yu, Y.1    Li, H.X.2
  • 23
    • 67650441690 scopus 로고    scopus 로고
    • Chaos in a fractional-order Rössler system
    • doi:10.1016/j.chaos.2009.03.069
    • Zhang, W, Zhou, S, Li, H, Zhu, H: Chaos in a fractional-order Rössler system. Chaos Solitons Fract. 42(3), 1684-1691 (2009). doi:10.1016/j.chaos.2009.03.069
    • (2009) Chaos Solitons Fract. , vol.42 , Issue.3 , pp. 1684-1691
    • Zhang, W.1    Zhou, S.2    Li, H.3    Zhu, H.4
  • 24
    • 63449114132 scopus 로고    scopus 로고
    • Controlling general projective synchronization of fractional order Rossler systems
    • doi:10.1016/j.chaos.2007.06.011
    • Shao, S: Controlling general projective synchronization of fractional order Rossler systems. Chaos Solitons Fract. 39(4), 1572-1577 (2009). doi:10.1016/j.chaos.2007.06.011
    • (2009) Chaos Solitons Fract. , vol.39 , Issue.4 , pp. 1572-1577
    • Shao, S.1
  • 25
    • 27744462122 scopus 로고    scopus 로고
    • Synchronization in fractional-order differential systems
    • doi:10.1016/j.physd.2005.09.012
    • Zhou, T, Li, C: Synchronization in fractional-order differential systems. Physica D Nonlinear Phenom. 212(1-2), 111-125 (2005). doi:10.1016/j.physd.2005. 09.012
    • (2005) Physica D Nonlinear Phenom. , vol.212 , Issue.1-2 , pp. 111-125
    • Zhou, T.1    Li, C.2
  • 26
    • 67349108727 scopus 로고    scopus 로고
    • Stability conditions, hyperchaos and control in a novel fractional order hyperchaotic system
    • doi:10.1016/j.physleta.2009.04.032
    • Matouk, AE: Stability conditions, hyperchaos and control in a novel fractional order hyperchaotic system. Phys Lett A. 373, 2166-2173 (2009). doi:10.1016/j.physleta.2009.04.032
    • (2009) Phys Lett A , vol.373 , pp. 2166-2173
    • Matouk, A.E.1
  • 27
    • 36348976811 scopus 로고    scopus 로고
    • Fractional calculus: A mathematical tool from the past for the present engineer
    • summer
    • Cafagna, D: Fractional calculus: a mathematical tool from the past for the present engineer. IEEE Industrial Electronic Magazine 35-40 (2007). summer
    • (2007) IEEE Industrial Electronic Magazine , vol.35-40
    • Cafagna, D.1
  • 28
    • 34247212711 scopus 로고    scopus 로고
    • Remarks on fractional derivatives
    • doi:10.1016/j.amc.2006.08.163
    • Li, C, Deng, W: Remarks on fractional derivatives. Appl Math Comput. 187, 777-784 (2007). doi:10.1016/j.amc.2006.08.163
    • (2007) Appl Math Comput. , vol.187 , pp. 777-784
    • Li, C.1    Deng, W.2
  • 29
    • 33847067879 scopus 로고    scopus 로고
    • Does the fractional Brusselator with efficient dimension less than 1 have a limit cycle?
    • doi:10.1016/j.physleta.2006.11.038
    • Wang, Y, Li, C: Does the fractional Brusselator with efficient dimension less than 1 have a limit cycle? Phys Lett A. 363, 414-419 (2007). doi:10.1016/j.physleta.2006.11.038
    • (2007) Phys Lett A , vol.363 , pp. 414-419
    • Wang, Y.1    Li, C.2
  • 30
    • 0002731965 scopus 로고    scopus 로고
    • Stability results for fractional differential equations with applications to control processing
    • IMACS, IEEE-SMC Proceedings Lille, France
    • Matignon, D: Stability results for fractional differential equations with applications to control processing. in Computational Engineering in Systems and Application Multi-conference, vol. 2, IMACS, IEEE-SMC Proceedings. pp. 963-968. Lille, France (1996)
    • (1996) Computational Engineering in Systems and Application Multi-conference , vol.2 , pp. 963-968
    • Matignon, D.1
  • 31
    • 33947133956 scopus 로고    scopus 로고
    • Stability analysis of linear fractional differential system with multiple time delays
    • doi:10.1007/s11071-006-9094-0
    • Deng, W, Li, C, Lu, J: Stability analysis of linear fractional differential system with multiple time delays. Nonlinear Dyn. 48, 409-416 (2007). doi:10.1007/s11071-006-9094-0
    • (2007) Nonlinear Dyn. , vol.48 , pp. 409-416
    • Deng, W.1    Li, C.2    Lu, J.3
  • 32
    • 0036650479 scopus 로고    scopus 로고
    • A predictor-corrector approach for the numerical solution of fractional differential equations
    • doi:10.1023/A:1016592219341
    • Diethelm, K, Ford, NJ, Freed, AD: A predictor-corrector approach for the numerical solution of fractional differential equations. Nonlinear Dyn. 29, 3-22 (2002). doi:10.1023/A:1016592219341
    • (2002) Nonlinear Dyn. , vol.29 , pp. 3-22
    • Diethelm, K.1    Ford, N.J.2    Freed, A.D.3
  • 33
    • 0001618393 scopus 로고    scopus 로고
    • An algorithm for the numerical solution of differential equations of fractional order
    • Diethelm, K: An algorithm for the numerical solution of differential equations of fractional order. Electron Trans. Numer Anal. 5, 1-6 (1997)
    • (1997) Electron Trans. Numer Anal. , vol.5 , pp. 1-6
    • Diethelm, K.1
  • 34
    • 0037081673 scopus 로고    scopus 로고
    • Analysis of fractional differential equations
    • doi:10.1006/jmaa.2000.7194
    • Diethelm, K, Ford, NJ: Analysis of fractional differential equations. J Math Anal Appl. 265, 229-248 (2002). doi:10.1006/jmaa.2000.7194
    • (2002) J Math Anal Appl. , vol.265 , pp. 229-248
    • Diethelm, K.1    Ford, N.J.2
  • 35
    • 43949139899 scopus 로고    scopus 로고
    • On existence and local attractivity of solutions of a quadratic Volterra integral equation of fractional order
    • doi:10.1016/j.jmaa.2008.04.050
    • Banaś, J, O'Regan, D: On existence and local attractivity of solutions of a quadratic Volterra integral equation of fractional order. J Math Anal Appl. 345(1), 573-582 (2008). doi:10.1016/j.jmaa.2008.04.050
    • (2008) J Math Anal Appl. , vol.345 , Issue.1 , pp. 573-582
    • Banaś, J.1    O'Regan, D.2
  • 36
    • 49549126801 scopus 로고
    • An equation for continuous chaos
    • doi:10.1016/0375-9601(76)90101-8
    • Rössler, OE: An equation for continuous chaos. Phys Lett A. 57(5), 397-398 (1976). doi:10.1016/0375-9601(76)90101-8
    • (1976) Phys Lett A , vol.57 , Issue.5 , pp. 397-398
    • Rössler, O.E.1
  • 37
    • 3342927052 scopus 로고    scopus 로고
    • Chaos and hyperchaos in the fractional order Rössler equations
    • Li, C, Chen, G: Chaos and hyperchaos in the fractional order Rössler equations. Physica A. 341, 55-61 (2004)
    • (2004) Physica A , vol.341 , pp. 55-61
    • Li, C.1    Chen, G.2
  • 38
    • 51249088596 scopus 로고    scopus 로고
    • Chaotic attractors in incommensurate fractional order systems
    • doi:10.1016/j.physd.2008.03.037
    • Tavazoei, MS, Haeri, M: Chaotic attractors in incommensurate fractional order systems. Physica D. 237, 2628-2637 (2008). doi:10.1016/j.physd.2008.03.037
    • (2008) Physica D , vol.237 , pp. 2628-2637
    • Tavazoei, M.S.1    Haeri, M.2


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