메뉴 건너뛰기




Volumn 68, Issue 1-2, 2012, Pages 117-128

Observer-based projective synchronization of fractional systems via a scalar signal: Application to hyperchaotic Rössler systems

Author keywords

Chaos; Fractional order systems; Hyperchaotic R ssler system; Projective synchronization; Scalar synchronizing signal

Indexed keywords

ERROR DYNAMICS; EXACT ANALYTICAL SOLUTIONS; FRACTIONAL ERRORS; FRACTIONAL SYSTEMS; FRACTIONAL-ORDER CHAOTIC SYSTEMS; FRACTIONAL-ORDER SYSTEMS; HYPERCHAOTIC; MITTAG-LEFFLER FUNCTIONS; PROJECTIVE SYNCHRONIZATION; SCALAR SIGNAL; SYNCHRONIZING SIGNAL; THEORETICAL FOUNDATIONS;

EID: 84858706326     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-011-0208-y     Document Type: Article
Times cited : (64)

References (51)
  • 1
    • 0343689904 scopus 로고
    • Synchronization in chaotic systems
    • 1038263 10.1103/PhysRevLett.64.821
    • L.M. Pecora T.L. Carrol 1990 Synchronization in chaotic systems Phys. Rev. Lett. 64 821 824 1038263 10.1103/PhysRevLett.64.821
    • (1990) Phys. Rev. Lett. , vol.64 , pp. 821-824
    • Pecora, L.M.1    Carrol, T.L.2
  • 2
    • 0001177874 scopus 로고    scopus 로고
    • Synchronizing hyperchaos with a scalar transmitted signal
    • J.H. Peng E.J. Ding M. Ding W. Yang 1996 Synchronizing hyperchaos with a scalar transmitted signal Phys. Rev. Lett. 76 904 907 10.1103/PhysRevLett.76.904 (Pubitemid 126618495)
    • (1996) Physical Review Letters , vol.76 , Issue.6 , pp. 904-907
    • Peng, J.H.1    Ding, E.J.2    Ding, M.3    Yang, W.4
  • 7
    • 0032485167 scopus 로고    scopus 로고
    • Synchronisation of hyperchaotic oscillators using a scalar signal
    • G. Grassi S. Mascolo 1998 Synchronization of hyperchaotic oscillators using a scalar signal IEE Electron. Lett. 34 424 425 10.1049/el:19980099 (Pubitemid 128561599)
    • (1998) Electronics Letters , vol.34 , Issue.5 , pp. 424-425
    • Grassi, G.1    Mascolo, S.2
  • 8
    • 0000777715 scopus 로고    scopus 로고
    • Projective synchronization in three-dimensional chaotic systems
    • R. Mainieri J. Rehacek 1999 Projective synchronization in three-dimensional chaotic systems Phys. Rev. Lett. 82 3042 3045 10.1103/PhysRevLett.82.3042 (Pubitemid 129689207)
    • (1999) Physical Review Letters , vol.82 , Issue.15 , pp. 3042-3045
    • Mainieri, R.1    Rehacek, J.2
  • 9
    • 17644410408 scopus 로고    scopus 로고
    • Nonlinear observer control for full-state projective synchronization in chaotic continuous-time systems
    • DOI 10.1016/j.chaos.2004.09.117, PII S0960077904006265
    • G. Wen D. Xu 2005 Nonlinear observer control for full-state projective synchronization in chaotic continuous-time systems Chaos Solitons Fractals 26 71 77 2102792 1122.93311 10.1016/j.chaos.2004.09.117 (Pubitemid 40556370)
    • (2005) Chaos, Solitons and Fractals , vol.26 , Issue.1 , pp. 71-77
    • Wen, G.1    Xu, D.2
  • 10
    • 34250171746 scopus 로고    scopus 로고
    • Projective synchronization via a linear observer: Application to time-delay, continuous-time and discrete-time systems
    • DOI 10.1142/S0218127407017835, PII S0218127407017835
    • G. Grassi D.A. Miller 2007 Projective synchronization via a linear observer: application to time-delay, continuous-time and discrete-time systems Int. J. Bifurc. Chaos 17 1337 1342 2329526 1139.93348 10.1142/S0218127407017835 (Pubitemid 46905055)
    • (2007) International Journal of Bifurcation and Chaos , vol.17 , Issue.4 , pp. 1337-1342
    • Grassi, G.1    Miller, D.A.2
  • 11
    • 62949181226 scopus 로고    scopus 로고
    • Arbitrary observer scaling of all chaotic drive system states via a scalar synchronizing signal
    • 1197.37135 10.1016/j.chaos.2007.06.002
    • G. Grassi D.A. Miller 2009 Arbitrary observer scaling of all chaotic drive system states via a scalar synchronizing signal Chaos Solitons Fractals 39 1246 1252 1197.37135 10.1016/j.chaos.2007.06.002
    • (2009) Chaos Solitons Fractals , vol.39 , pp. 1246-1252
    • Grassi, G.1    Miller, D.A.2
  • 12
    • 0041384356 scopus 로고    scopus 로고
    • Chaotic dynamics of the fractional Lorenz system
    • 10.1103/PhysRevLett.91.034101
    • I. Grigorenko E. Grigorenko 2003 Chaotic dynamics of the fractional Lorenz system Phys. Rev. Lett. 91 34101 10.1103/PhysRevLett.91.034101
    • (2003) Phys. Rev. Lett. , vol.91 , pp. 34101
    • Grigorenko, I.1    Grigorenko, E.2
  • 13
    • 3342927052 scopus 로고    scopus 로고
    • Chaos and hyperchaos in the fractional-order Rössler equations
    • 2092674 10.1016/j.physa.2004.04.113
    • C.G. Li G.R. Chen 2004 Chaos and hyperchaos in the fractional-order Rössler equations Physica A 341 55 61 2092674 10.1016/j.physa.2004.04.113
    • (2004) Physica A , vol.341 , pp. 55-61
    • Li, C.G.1    Chen, G.R.2
  • 14
    • 65249109832 scopus 로고    scopus 로고
    • Hyperchaos in the fractional-order Rössler system with lowest-order
    • 1170.34327 10.1142/S0218127409022890
    • D. Cafagna G. Grassi 2009 Hyperchaos in the fractional-order Rössler system with lowest-order Int. J. Bifurc. Chaos 19 339 347 1170.34327 10.1142/S0218127409022890
    • (2009) Int. J. Bifurc. Chaos , vol.19 , pp. 339-347
    • Cafagna, D.1    Grassi, G.2
  • 16
    • 45149102412 scopus 로고    scopus 로고
    • Fractional-order Chua's circuit: Time-domain analysis, bifurcation, chaotic behavior and test for chaos
    • DOI 10.1142/S0218127408020550, PII S0218127408020550
    • D. Cafagna G. Grassi 2008 Fractional-order Chua's circuit: time-domain analysis, bifurcation, chaotic behaviour and test for chaos Int. J. Bifurc. Chaos 18 615 639 2415859 1147.34302 10.1142/S0218127408020550 (Pubitemid 351828395)
    • (2008) International Journal of Bifurcation and Chaos , vol.18 , Issue.3 , pp. 615-639
    • Cafagna, D.1    Grassi, G.2
  • 17
    • 2042470796 scopus 로고    scopus 로고
    • Chaos in the fractional-order Chen system and its control
    • 1069.37025 10.1016/j.chaos.2004.02.035
    • C.G. Li G. Chen 2004 Chaos in the fractional-order Chen system and its control Chaos Solitons Fractals 22 549 554 1069.37025 10.1016/j.chaos.2004.02. 035
    • (2004) Chaos Solitons Fractals , vol.22 , pp. 549-554
    • Li, C.G.1    Chen, G.2
  • 18
    • 52149110344 scopus 로고    scopus 로고
    • Bifurcation and chaos in the fractional-order Chen system via a time-domain approach
    • 2454066 1158.34300 10.1142/S0218127408021415
    • D. Cafagna G. Grassi 2008 Bifurcation and chaos in the fractional-order Chen system via a time-domain approach Int. J. Bifurc. Chaos 18 1845 1863 2454066 1158.34300 10.1142/S0218127408021415
    • (2008) Int. J. Bifurc. Chaos , vol.18 , pp. 1845-1863
    • Cafagna, D.1    Grassi, G.2
  • 19
    • 18844427587 scopus 로고    scopus 로고
    • Chaos synchronization of the fractional Lü system
    • DOI 10.1016/j.physa.2005.01.021, PII S0378437105000555
    • W.H. Deng C.P. Li 2005 Chaos synchronization of the fractional Lu system Physica A 353 61 72 10.1016/j.physa.2005.01.021 (Pubitemid 40684290)
    • (2005) Physica A: Statistical Mechanics and its Applications , vol.353 , Issue.1-4 , pp. 61-72
    • Deng, W.H.1    Li, C.P.2
  • 20
    • 27744554781 scopus 로고    scopus 로고
    • Chaos synchronization of the Chua system with a fractional order
    • DOI 10.1016/j.physa.2005.06.078, PII S0378437105007132
    • C.P. Li W.H. Deng D. Xu 2006 Chaos synchronization of the Chua system with a fractional order Physica A 360 171 185 2186261 10.1016/j.physa.2005.06. 078 (Pubitemid 41627568)
    • (2006) Physica A: Statistical Mechanics and its Applications , vol.360 , Issue.2 , pp. 171-185
    • Li, C.P.1    Deng, W.H.2    Xu, D.3
  • 21
    • 35748971445 scopus 로고    scopus 로고
    • Synchronization of chaotic fractional-order systems via active sliding mode controller
    • DOI 10.1016/j.physa.2007.08.039, PII S0378437107008849
    • M.S. Tavazoei M. Haeri 2008 Synchronization of chaotic fractional-order systems via active sliding mode controller Physica A 387 57 70 2514122 10.1016/j.physa.2007.08.039 (Pubitemid 350051260)
    • (2008) Physica A: Statistical Mechanics and its Applications , vol.387 , Issue.1 , pp. 57-70
    • Tavazoei, M.S.1    Haeri, M.2
  • 22
    • 67649319511 scopus 로고    scopus 로고
    • Chaos synchronization of the fractional-order Chen's system
    • 1198.93206 10.1016/j.chaos.2008.10.005
    • H. Zhu S. Zhou Z. He 2009 Chaos synchronization of the fractional-order Chen's system Chaos Solitons Fractals 41 2733 2740 1198.93206 10.1016/j.chaos.2008.10.005
    • (2009) Chaos Solitons Fractals , vol.41 , pp. 2733-2740
    • Zhu, H.1    Zhou, S.2    He, Z.3
  • 23
    • 67849086834 scopus 로고    scopus 로고
    • Synchronizing chaotic systems using control based on a special matrix structure and extending to fractional chaotic systems
    • 2567061 1221.37212 10.1016/j.cnsns.2009.03.017
    • J. Hu Y. Han L. Zhao 2010 Synchronizing chaotic systems using control based on a special matrix structure and extending to fractional chaotic systems Commun. Nonlinear Sci. Numer. Simul. 15 115 123 2567061 1221.37212 10.1016/j.cnsns.2009.03.017
    • (2010) Commun. Nonlinear Sci. Numer. Simul. , vol.15 , pp. 115-123
    • Hu, J.1    Han, Y.2    Zhao, L.3
  • 24
    • 43049112743 scopus 로고    scopus 로고
    • Generalized projective synchronization of a class of fractional-order chaotic systems via a scalar transmitted signal
    • 2418398 1220.34060 10.1016/j.physleta.2008.01.061
    • G.J. Peng Y.L. Jiang 2008 Generalized projective synchronization of a class of fractional-order chaotic systems via a scalar transmitted signal Phys. Lett. A 372 3963 3970 2418398 1220.34060 10.1016/j.physleta.2008.01.061
    • (2008) Phys. Lett. A , vol.372 , pp. 3963-3970
    • Peng, G.J.1    Jiang, Y.L.2
  • 25
    • 78649364156 scopus 로고    scopus 로고
    • A new scheme to projective synchronization of fractional-order chaotic systems
    • 10.1088/0256-307X/27/11/110501
    • J.W. Wang A.M. Chen 2010 A new scheme to projective synchronization of fractional-order chaotic systems Chin. Phys. Lett. 27 110501 10.1088/0256-307X/27/11/110501
    • (2010) Chin. Phys. Lett. , vol.27 , pp. 110501
    • Wang, J.W.1    Chen, A.M.2
  • 26
    • 36448973733 scopus 로고    scopus 로고
    • Projective synchronization in coupled fractional order chaotic Rossler system and its control
    • DOI 10.1088/1009-1963/16/9/019
    • S.Q. Shao X. Gao X.W. Liu 2007 Projective synchronization in coupled fractional order chaotic Rossler system and its control Chin. Phys. 16 2612 10.1088/1009-1963/16/9/019 (Pubitemid 350205133)
    • (2007) Chinese Physics , vol.16 , Issue.9 , pp. 2612-2615
    • Shao, S.-Q.1    Gao, X.2    Liu, X.-W.3
  • 27
    • 78651062020 scopus 로고    scopus 로고
    • Dynamic analysis of a new chaotic system with fractional order and its generalized projective synchronization
    • 10.1088/1674-1056/19/12/120507
    • Y.J. Niu X.Y. Wang F.Z. Nian M.J. Wang 2010 Dynamic analysis of a new chaotic system with fractional order and its generalized projective synchronization Chin. Phys. B 19 120507 10.1088/1674-1056/19/12/120507
    • (2010) Chin. Phys. B , vol.19 , pp. 120507
    • Niu, Y.J.1    Wang, X.Y.2    Nian, F.Z.3    Wang, M.J.4
  • 28
    • 77952741594 scopus 로고    scopus 로고
    • Chaos in fractional conjugate Lorenz system and its scaling attractors
    • 2652675 1222.37037 10.1016/j.cnsns.2010.02.005
    • Q. Yang C. Zeng 2010 Chaos in fractional conjugate Lorenz system and its scaling attractors Commun. Nonlinear Sci. Numer. Simul. 15 4041 4051 2652675 1222.37037 10.1016/j.cnsns.2010.02.005
    • (2010) Commun. Nonlinear Sci. Numer. Simul. , vol.15 , pp. 4041-4051
    • Yang, Q.1    Zeng, C.2
  • 29
    • 63449114132 scopus 로고    scopus 로고
    • Controlling general projective synchronization of fractional order Rössler systems
    • 1197.37041 10.1016/j.chaos.2007.06.011
    • S. Shao 2009 Controlling general projective synchronization of fractional order Rössler systems Chaos Solitons Fractals 39 1572 1577 1197.37041 10.1016/j.chaos.2007.06.011
    • (2009) Chaos Solitons Fractals , vol.39 , pp. 1572-1577
    • Shao, S.1
  • 30
    • 67449143115 scopus 로고    scopus 로고
    • Generalized projective synchronization of the fractional-order Chen hyperchaotic system
    • 1176.70029 10.1007/s11071-008-9416-5
    • X. Wu Y. Lu 2009 Generalized projective synchronization of the fractional-order Chen hyperchaotic system Nonlinear Dyn. 57 25 35 1176.70029 10.1007/s11071-008-9416-5
    • (2009) Nonlinear Dyn. , vol.57 , pp. 25-35
    • Wu, X.1    Lu, Y.2
  • 31
    • 77956595176 scopus 로고    scopus 로고
    • A new chaotic system with fractional order and its projective synchronization
    • 1204.37035 10.1007/s11071-010-9658-x
    • X. Wu H. Wang 2010 A new chaotic system with fractional order and its projective synchronization Nonlinear Dyn. 61 407 417 1204.37035 10.1007/s11071-010-9658-x
    • (2010) Nonlinear Dyn. , vol.61 , pp. 407-417
    • Wu, X.1    Wang, H.2
  • 32
    • 78049454811 scopus 로고    scopus 로고
    • Chaos and hybrid projective synchronization of commensurate and incommensurate fractional-order Chen-Lee systems
    • 2745945 1215.37024 10.1007/s11071-010-9767-6
    • C.M. Chang H.K. Chen 2010 Chaos and hybrid projective synchronization of commensurate and incommensurate fractional-order Chen-Lee systems Nonlinear Dyn. 62 851 858 2745945 1215.37024 10.1007/s11071-010-9767-6
    • (2010) Nonlinear Dyn. , vol.62 , pp. 851-858
    • Chang, C.M.1    Chen, H.K.2
  • 34
    • 0002847893 scopus 로고    scopus 로고
    • Fractional calculus: Integral and differential equations of fractional order
    • Springer Wien
    • Gorenflo, R., Mainardi, F.: Fractional calculus: integral and differential equations of fractional order. In: Fractal and Fractional Calculus in Continuum Mechanics, pp. 223-276. Springer, Wien (1997)
    • (1997) Fractal and Fractional Calculus in Continuum Mechanics , pp. 223-276
    • Gorenflo, R.1    Mainardi, F.2
  • 35
    • 84977255207 scopus 로고
    • Linear models of dissipation whose Q is almost frequency independent
    • 10.1111/j.1365-246X.1967.tb02303.x
    • M. Caputo 1967 Linear models of dissipation whose Q is almost frequency independent Geophys. J. R. Astron. Soc. 13 529 539 10.1111/j.1365-246X.1967. tb02303.x
    • (1967) Geophys. J. R. Astron. Soc. , vol.13 , pp. 529-539
    • Caputo, M.1
  • 37
    • 74149090385 scopus 로고    scopus 로고
    • Analytic study on linear systems of fractional differential equations
    • 2579481 1189.34017 10.1016/j.camwa.2009.06.035
    • Z.M. Odibat 2010 Analytic study on linear systems of fractional differential equations Comput. Math. Appl. 59 1171 1183 2579481 1189.34017 10.1016/j.camwa.2009.06.035
    • (2010) Comput. Math. Appl. , vol.59 , pp. 1171-1183
    • Odibat, Z.M.1
  • 38
    • 34247394106 scopus 로고    scopus 로고
    • On systems of linear fractional differential equations with constant coefficients
    • DOI 10.1016/j.amc.2006.08.104, PII S0096300306011386
    • B. Bonilla M. Rivero J.J. Trujillo 2007 On systems of linear fractional differential equations with constant coefficients Appl. Math. Comput. 187 68 78 2323556 1121.34006 10.1016/j.amc.2006.08.104 (Pubitemid 46635705)
    • (2007) Applied Mathematics and Computation , vol.187 , Issue.1 , pp. 68-78
    • Bonilla, B.1    Rivero, M.2    Trujillo, J.J.3
  • 39
    • 19144371559 scopus 로고    scopus 로고
    • Chaotic dynamics and synchronization of fractional-order Arneodo's systems
    • DOI 10.1016/j.chaos.2005.02.023, PII S0960077905001967
    • J.G. Lu 2005 Chaotic dynamics and synchronization of fractional-order Arneodo's systems Chaos Solitons Fractals 27 1125 1133 10.1016/j.chaos.2005.02. 023 (Pubitemid 40715537)
    • (2005) Chaos, Solitons and Fractals , vol.26 , Issue.4 , pp. 1125-1133
    • Lu, J.G.1
  • 41
    • 0000548789 scopus 로고
    • An equation for hyperchaos
    • 588951 0996.37502 10.1016/0375-9601(79)90150-6
    • O.E. Rössler 1979 An equation for hyperchaos Phys. Lett. A 71 155 157 588951 0996.37502 10.1016/0375-9601(79)90150-6
    • (1979) Phys. Lett. A , vol.71 , pp. 155-157
    • Rössler, O.E.1
  • 42
    • 34748892339 scopus 로고    scopus 로고
    • Synchronization of uncertain chaotic systems using a single transmission channel
    • DOI 10.1016/j.chaos.2006.05.097, PII S0960077906005108
    • Y. Feng X. Yu L. Sun 2008 Synchronization of uncertain chaotic systems using a single transmission channel Chaos Solitons Fractals 35 755 762 10.1016/j.chaos.2006.05.097 (Pubitemid 47484436)
    • (2008) Chaos, Solitons and Fractals , vol.35 , Issue.4 , pp. 755-762
    • Feng, Y.1    Yu, X.2    Sun, L.3
  • 44
    • 0032485167 scopus 로고    scopus 로고
    • Synchronisation of hyperchaotic oscillators using a scalar signal
    • G. Grassi S. Mascolo 1998 Synchronization of hyperchaotic oscillators using a scalar signal IEE Electron. Lett. 34 424 425 10.1049/el:19980099 (Pubitemid 128561599)
    • (1998) Electronics Letters , vol.34 , Issue.5 , pp. 424-425
    • Grassi, G.1    Mascolo, S.2
  • 45
    • 4644244178 scopus 로고    scopus 로고
    • Secure digital communication using controlled projective synchronisation of chaos
    • 1068.94010
    • C.Y. Chee D. Xu 2005 Secure digital communication using controlled projective synchronisation of chaos Chaos Solitons Fractals 23 1063 1070 1068.94010
    • (2005) Chaos Solitons Fractals , vol.23 , pp. 1063-1070
    • Chee, C.Y.1    Xu, D.2
  • 46
    • 33749830181 scopus 로고    scopus 로고
    • Chaos-based M-ary digital communication technique using controlled projective synchronisation
    • DOI 10.1049/ip-cds:20050139
    • C.Y. Chee D. Xu 2006 Chaos-based M-ary digital communication technique using controlled projective synchronization IEE Proc., Circuits Devices Syst. 153 357 360 10.1049/ip-cds:20050139 (Pubitemid 44561800)
    • (2006) IEE Proceedings: Circuits, Devices and Systems , vol.153 , Issue.4 , pp. 357-360
    • Chee, C.Y.1    Xu, D.2
  • 47
    • 47249084353 scopus 로고    scopus 로고
    • Modeling of electrochemical double layer capacitors by means of fractional impedance
    • R. Martin J. Quintana 2008 Modeling of electrochemical double layer capacitors by means of fractional impedance J. Comput. Nonlinear Dyn. 3 1303 1309
    • (2008) J. Comput. Nonlinear Dyn. , vol.3 , pp. 1303-1309
    • Martin, R.1    Quintana, J.2
  • 48
    • 47749106020 scopus 로고    scopus 로고
    • Fractional-order sinusoidal oscillators: Four practical circuit design examples
    • 1191.94175 10.1002/cta.453
    • A.G. Radwan A.M. Soliman A.S. Elwakil 2008 Fractional-order sinusoidal oscillators: Four practical circuit design examples Int. J. Circuit Theory Appl. 36 473 492 1191.94175 10.1002/cta.453
    • (2008) Int. J. Circuit Theory Appl. , vol.36 , pp. 473-492
    • Radwan, A.G.1    Soliman, A.M.2    Elwakil, A.S.3
  • 49
    • 75549084493 scopus 로고    scopus 로고
    • On a multivibrator that employs a fractional capacitor
    • 10.1007/s10470-009-9329-3
    • B. Maundy A. Elwakil S. Gift 2010 On a multivibrator that employs a fractional capacitor J. Analog Integr. Circuits Signal Process. 62 99 103 10.1007/s10470-009-9329-3
    • (2010) J. Analog Integr. Circuits Signal Process. , vol.62 , pp. 99-103
    • Maundy, B.1    Elwakil, A.2    Gift, S.3
  • 50
    • 78649591986 scopus 로고    scopus 로고
    • Fractional-order circuits and systems: An emerging interdisciplinary research area
    • 10.1109/MCAS.2010.938637
    • A.S. Elwakil 2010 Fractional-order circuits and systems: an emerging interdisciplinary research area IEEE Circuits Syst. Mag. 4 40 50 10.1109/MCAS.2010.938637
    • (2010) IEEE Circuits Syst. Mag. , vol.4 , pp. 40-50
    • Elwakil, A.S.1
  • 51
    • 79959528048 scopus 로고    scopus 로고
    • A speech encryption using fractional chaotic systems
    • 2812012 10.1007/s11071-010-9877-1
    • L.J. Sheu 2011 A speech encryption using fractional chaotic systems Nonlinear Dyn. 65 103 108 2812012 10.1007/s11071-010-9877-1
    • (2011) Nonlinear Dyn. , vol.65 , pp. 103-108
    • Sheu, L.J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.