메뉴 건너뛰기
Nonlinear Dynamics
Volumn 70, Issue 1, 2012, Pages 475-479
Studying on the stability of fractional-order nonlinear system
Author keywords

Decay rate; Fractional; Jacobian matrix; Mittag Leffler; Stability
Indexed keywords

DECAY RATE; EIGEN-VALUE; FRACTIONAL; MAXIMUM NORM; MITTAG-LEFFLER; MITTAG-LEFFLER FUNCTIONS; SIMPLE APPROACH;
EID: 84867897789     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-012-0469-0     Document Type: Article
Times cited : (28)
References (17)
  • 1
    • 79951578411 scopus 로고    scopus 로고
    • The parametric synchronization scheme of chaotic system
    • 2772307 1221.93129 10.1016/j.cnsns.2010.10.027
    • Li, Z.B.; Zhao, X.S.: The parametric synchronization scheme of chaotic system. Commun. Nonlinear Sci. Numer. Simul. 16, 2936-2940 (2011)
    • (2011) Commun. Nonlinear Sci. Numer. Simul. , vol.16 , pp. 2936-2940
    • Li, Z.B.1    Zhao, X.S.2
  • 2
    • 67649626081 scopus 로고    scopus 로고
    • Mittag-Leffler stability of fractional order nonlinear dynamic systems
    • 2879525 1185.93062 10.1016/j.automatica.2009.04.003
    • Li, Y.; Chen, Y.Q.; Podlubny, I.: Mittag-Leffler stability of fractional order nonlinear dynamic systems. Automatica 45, 1965-1969 (2009)
    • (2009) Automatica , vol.45 , pp. 1965-1969
    • Li, Y.1    Chen, Y.Q.2    Podlubny, I.3
  • 3
    • 78049324242 scopus 로고    scopus 로고
    • Studies on fractional order differentiators and integrators. A survey
    • 1203.94035 10.1016/j.sigpro.2010.06.022
    • Krishna, B.T.: Studies on fractional order differentiators and integrators. A survey. Signal Process. 91, 386-426 (2011)
    • (2011) Signal Process. , vol.91 , pp. 386-426
    • Krishna, B.T.1
  • 4
    • 70350738926 scopus 로고    scopus 로고
    • The fractional diffusion model with an absorption term and modified Fick's law for non-local transport processes
    • 2570546
    • Jiang, X.; Xu, M.; Qi, H.: The fractional diffusion model with an absorption term and modified Fick's law for non-local transport processes. Nonlinear Anal.; Real World Appl. 10, 262-270 (2009)
    • (2009) Nonlinear Anal.; Real World Appl. , vol.10 , pp. 262-270
    • Jiang, X.1    Xu, M.2    Qi, H.3
  • 5
    • 63449084428 scopus 로고    scopus 로고
    • Pinning control of fractional-order weighted complex networks
    • 013112 10.1063/1.3068350 2513760 10.1063/1.3068350
    • Tang, Y.; Wang, Z.D.; Fang, J.A.: Pinning control of fractional-order weighted complex networks. Chaos 19, 013112 (2009). doi: 10.1063/1.3068350
    • (2009) Chaos , vol.19
    • Tang, Y.1    Wang, Z.D.2    Fang, J.A.3
  • 6
    • 70349811334 scopus 로고    scopus 로고
    • Chaotic fractional-order Coullet system: Synchronization and control approach
    • 2572199 1221.37222 10.1016/j.cnsns.2009.05.054
    • Shahiri, M.; Ghaderi, R.; Ranjbar, N.; Hosseinnia, S.; Momani, S.: Chaotic fractional-order Coullet system: synchronization and control approach. Commun. Nonlinear Sci. Numer. Simul. 15, 665-674 (2010)
    • (2010) Commun. Nonlinear Sci. Numer. Simul. , vol.15 , pp. 665-674
    • Shahiri, M.1    Ghaderi, R.2    Ranjbar, N.3    Hosseinnia, S.4    Momani, S.5
  • 7
    • 70350367184 scopus 로고    scopus 로고
    • Fractional calculus in viscoelasticity: An experimental study
    • 2557002 1221.74012 10.1016/j.cnsns.2009.05.004
    • Meral, F.; Royston, T.; Magin, R.: Fractional calculus in viscoelasticity: an experimental study. Commun. Nonlinear Sci. Numer. Simul. 15, 939-945 (2010)
    • (2010) Commun. Nonlinear Sci. Numer. Simul. , vol.15 , pp. 939-945
    • Meral, F.1    Royston, T.2    Magin, R.3
  • 8
    • 34247477202 scopus 로고    scopus 로고
    • On fractional order differential equations model for nonlocal epidemics
    • 2288095 10.1016/j.physa.2007.01.010
    • Ahmed, E.; Elgazzar, A.S.: On fractional order differential equations model for nonlocal epidemics. Physica A 379, 607-614 (2007)
    • (2007) Physica A , vol.379 , pp. 607-614
    • Ahmed, E.1    Elgazzar, A.S.2
  • 9
    • 33947164737 scopus 로고    scopus 로고
    • Fractional-order dynamical models of love
    • 2318922 1133.91539 10.1016/j.chaos.2006.01.098
    • Ahmad, W.; El-Khazali, R.: Fractional-order dynamical models of love. Chaos Solitons Fractals 33, 1367-1375 (2007)
    • (2007) Chaos Solitons Fractals , vol.33 , pp. 1367-1375
    • Ahmad, W.1    El-Khazali, R.2
  • 10
    • 70349789880 scopus 로고    scopus 로고
    • Dynamical models of happiness with fractional order
    • 2572195 1221.93234 10.1016/j.cnsns.2009.04.029
    • Song, L.; Xu, S.; Yang, J.: Dynamical models of happiness with fractional order. Commun. Nonlinear Sci. Numer. Simul. 15, 616-628 (2010)
    • (2010) Commun. Nonlinear Sci. Numer. Simul. , vol.15 , pp. 616-628
    • Song, L.1    Xu, S.2    Yang, J.3
  • 11
    • 82255193992 scopus 로고    scopus 로고
    • Control of a class of fractional-order chaotic systems via sliding mode
    • 10.1007/s11071-011-0002-x
    • Chen, D.Y.; Liu, Y.X.; Ma, X.Y.: Control of a class of fractional-order chaotic systems via sliding mode. Nonlinear Dyn. 6(7), 893-901 (2012)
    • (2012) Nonlinear Dyn. , vol.6 , Issue.7 , pp. 893-901
    • Chen, D.Y.1    Liu, Y.X.2    Ma, X.Y.3
  • 12
    • 69049091852 scopus 로고    scopus 로고
    • Synchronization of N-coupled fractional-order chaotic systems with ring connection
    • 2572572 1221.34103 10.1016/j.cnsns.2009.03.024
    • Tang, Y.; Fang, J.A.: Synchronization of N-coupled fractional-order chaotic systems with ring connection. Commun. Nonlinear Sci. Numer. Simul. 15, 401-412 (2010)
    • (2010) Commun. Nonlinear Sci. Numer. Simul. , vol.15 , pp. 401-412
    • Tang, Y.1    Fang, J.A.2
  • 13
    • 59549083651 scopus 로고    scopus 로고
    • Synchronizing fractional chaotic systems based on Lyapunov equation
    • 2516989 1199.37060
    • Hu, J.B.; Han, Y.; Zhao, L.D.: Synchronizing fractional chaotic systems based on Lyapunov equation. Acta Phys. Sin. 57, 7522-7526 (2008)
    • (2008) Acta Phys. Sin. , vol.57 , pp. 7522-7526
    • Hu, J.B.1    Han, Y.2    Zhao, L.D.3
  • 14
    • 77956773241 scopus 로고    scopus 로고
    • Mittag-Leffler stability theorem for fractional nonlinear systems with delay
    • 108651 2674391 10.1155/2010/108651
    • Sadati, S.J.; Baleanu, D.; Ranjbar, A.; Ghaderi, R.; Abdeljawad: Mittag-Leffler stability theorem for fractional nonlinear systems with delay. Abstr. Appl. Anal. 2010, 108651 (2010)
    • (2010) Abstr. Appl. Anal. , vol.2010
    • Sadati, S.J.1    Baleanu, D.2    Ranjbar, A.3    Ghaderi, R.4    Abdeljawad5
  • 15
    • 84977255207 scopus 로고
    • Linear models of dissipation whose Q is almost frequency independent. Part II
    • 10.1111/j.1365-246X.1967.tb02303.x
    • Caputo, M.: Linear models of dissipation whose Q is almost frequency independent. Part II. J. R. Aust. Soc. 13, 529-539 (1967)
    • (1967) J. R. Aust. Soc. , vol.13 , pp. 529-539
    • Caputo, M.1
  • 16
    • 2442548776 scopus 로고    scopus 로고
    • Analysis of a system of fractional differential equations
    • 2053894 1058.34002 10.1016/j.jmaa.2004.01.013
    • Daftardar-Gejji, V.; Babakhani, A.: Analysis of a system of fractional differential equations. J. Math. Anal. Appl. 293, 511-522 (2004)
    • (2004) J. Math. Anal. Appl. , vol.293 , pp. 511-522
    • Daftardar-Gejji, V.1    Babakhani, A.2
  • 17
    • 77955559750 scopus 로고    scopus 로고
    • Two routes to chaos in the fractional Lorenz system with dimension continuously varying
    • 2671090 10.1016/j.physa.2010.05.037
    • Peng, G.J.; Jiang, Y.L.: Two routes to chaos in the fractional Lorenz system with dimension continuously varying. Physica A 389, 4140-4148 (2010)
    • (2010) Physica A , vol.389 , pp. 4140-4148
    • Peng, G.J.1    Jiang, Y.L.2

* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.