메뉴 건너뛰기




Volumn 34, Issue 2, 2007, Pages 262-291

Chaos in a fractional order modified Duffing system

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; BIFURCATION (MATHEMATICS); CONFORMAL MAPPING; FRACTALS; FREQUENCY DOMAIN ANALYSIS; NUMERICAL METHODS; TRANSFER FUNCTIONS;

EID: 34147144036     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2005.11.059     Document Type: Article
Times cited : (148)

References (27)
  • 1
    • 18844436776 scopus 로고    scopus 로고
    • What is the exact condition for fractional integrals and derivatives of Besicovitch functions to have exact box dimension?
    • He G.L., and Zhou S.P. What is the exact condition for fractional integrals and derivatives of Besicovitch functions to have exact box dimension?. Chaos, Solitons & Fractals 26 (2005) 867-879
    • (2005) Chaos, Solitons & Fractals , vol.26 , pp. 867-879
    • He, G.L.1    Zhou, S.P.2
  • 2
    • 4243138250 scopus 로고    scopus 로고
    • On the connection between the order of fractional calculus and the dimensions of a fractal function
    • Yao K., Su W.Y., and Zhou S.P. On the connection between the order of fractional calculus and the dimensions of a fractal function. Chaos, Solitons & Fractals 23 (2005) 621-629
    • (2005) Chaos, Solitons & Fractals , vol.23 , pp. 621-629
    • Yao, K.1    Su, W.Y.2    Zhou, S.P.3
  • 3
    • 0035480489 scopus 로고    scopus 로고
    • Fractional master equation: non-standard analysis and Liouville-Riemann derivative
    • Guy J. Fractional master equation: non-standard analysis and Liouville-Riemann derivative. Chaos, Solitons & Fractals 12 (2001) 2577-2587
    • (2001) Chaos, Solitons & Fractals , vol.12 , pp. 2577-2587
    • Guy, J.1
  • 4
    • 0033197368 scopus 로고    scopus 로고
    • Fractional integral representation of master equation
    • Elwakil S.A., and Zahran M.A. Fractional integral representation of master equation. Chaos, Solitons & Fractals 10 (1999) 1545-1548
    • (1999) Chaos, Solitons & Fractals , vol.10 , pp. 1545-1548
    • Elwakil, S.A.1    Zahran, M.A.2
  • 8
    • 0033888365 scopus 로고    scopus 로고
    • Frequency band complex non integer differentiator: characterization and synthesis
    • Oustaloup A., Levron F., Nanot F., and Mathieu B. Frequency band complex non integer differentiator: characterization and synthesis. IEEE Trans CAS-I 47 (2000) 25-40
    • (2000) IEEE Trans CAS-I , vol.47 , pp. 25-40
    • Oustaloup, A.1    Levron, F.2    Nanot, F.3    Mathieu, B.4
  • 9
    • 0036506044 scopus 로고    scopus 로고
    • Discretization schemes for fractional-order differentiators and integrators
    • Chen Y.Q., and Moore K. Discretization schemes for fractional-order differentiators and integrators. IEEE Trans CAS-I 49 (2002) 363-367
    • (2002) IEEE Trans CAS-I , vol.49 , pp. 363-367
    • Chen, Y.Q.1    Moore, K.2
  • 10
    • 0036650827 scopus 로고    scopus 로고
    • Dynamics and control of initialized fractional-order systems
    • Hartley T.T., and Lorenzo C.F. Dynamics and control of initialized fractional-order systems. Nonlinear Dyn 29 (2002) 201-233
    • (2002) Nonlinear Dyn , vol.29 , pp. 201-233
    • Hartley, T.T.1    Lorenzo, C.F.2
  • 11
    • 0036530321 scopus 로고    scopus 로고
    • A note on time-domain simulation of feedback fractional-order systems
    • Hwang C., Leu J.F., and Tsay S.Y. A note on time-domain simulation of feedback fractional-order systems. IEEE Trans Autom Control 47 (2002) 625-631
    • (2002) IEEE Trans Autom Control , vol.47 , pp. 625-631
    • Hwang, C.1    Leu, J.F.2    Tsay, S.Y.3
  • 14
    • 34147167678 scopus 로고    scopus 로고
    • Arena P, Caponetto R, Fortuna L, Porto D. Chaos in a fractional order Duffing system. In: Proc ECCTD. Budapest; 1997. p. 1259-62.
  • 15
    • 0037332868 scopus 로고    scopus 로고
    • Chaos in fractional-order autonomous nonlinear systems
    • Ahmad W.M., and Sprott J.C. Chaos in fractional-order autonomous nonlinear systems. Chaos, Solitons & Fractals 16 (2003) 339-351
    • (2003) Chaos, Solitons & Fractals , vol.16 , pp. 339-351
    • Ahmad, W.M.1    Sprott, J.C.2
  • 16
    • 0038239773 scopus 로고    scopus 로고
    • On nonlinear control design for autonomous chaotic systems of integer and fractional orders
    • Ahmad W.M., and Harb W.M. On nonlinear control design for autonomous chaotic systems of integer and fractional orders. Chaos, Solitons & Fractals 18 (2003) 693-701
    • (2003) Chaos, Solitons & Fractals , vol.18 , pp. 693-701
    • Ahmad, W.M.1    Harb, W.M.2
  • 17
    • 0035974637 scopus 로고    scopus 로고
    • Fractional-order Wien-bridge oscillator
    • Ahmad W., El-Khazali R., and El-Wakil A. Fractional-order Wien-bridge oscillator. Electron Lett 37 (2001) 1110-1112
    • (2001) Electron Lett , vol.37 , pp. 1110-1112
    • Ahmad, W.1    El-Khazali, R.2    El-Wakil, A.3
  • 18
    • 0041384356 scopus 로고    scopus 로고
    • Chaotic dynamics of the fractional Lorenz system
    • Grigorenko I., and Grigorenko E. Chaotic dynamics of the fractional Lorenz system. Phys Rev Lett 91 (2003) 034101
    • (2003) Phys Rev Lett , vol.91 , pp. 034101
    • Grigorenko, I.1    Grigorenko, E.2
  • 19
    • 0039504232 scopus 로고    scopus 로고
    • Bifurcation and chaos in noninteger order cellular neural networks
    • Arena P., Caponetto R., Fortuna L., and Porto D. Bifurcation and chaos in noninteger order cellular neural networks. Int J Bifurcat Chaos 7 (1998) 1527-1539
    • (1998) Int J Bifurcat Chaos , vol.7 , pp. 1527-1539
    • Arena, P.1    Caponetto, R.2    Fortuna, L.3    Porto, D.4
  • 20
    • 1442346520 scopus 로고    scopus 로고
    • Chaotic behavior in noninteger-order cellular neural networks
    • Arena P., Fortuna L., and Porto D. Chaotic behavior in noninteger-order cellular neural networks. Phys Rev E 61 (2000) 776-781
    • (2000) Phys Rev E , vol.61 , pp. 776-781
    • Arena, P.1    Fortuna, L.2    Porto, D.3
  • 21
    • 3342927052 scopus 로고    scopus 로고
    • Chaos and hyperchaos in fractional order Rössler equations
    • Li C.G., and Chen G. Chaos and hyperchaos in fractional order Rössler equations. Phycica A 341 (2004) 55-61
    • (2004) Phycica A , vol.341 , pp. 55-61
    • Li, C.G.1    Chen, G.2
  • 22
    • 2042470796 scopus 로고    scopus 로고
    • Chaos in the fractional order Chen system and its control
    • Li C.G., and Chen G. Chaos in the fractional order Chen system and its control. Chaos, Solitons & Fractals 22 (2004) 549-554
    • (2004) Chaos, Solitons & Fractals , vol.22 , pp. 549-554
    • Li, C.G.1    Chen, G.2
  • 23
    • 1842832060 scopus 로고    scopus 로고
    • Chaos in Chen's system with a fractional order
    • Li C.P., and Peng G.J. Chaos in Chen's system with a fractional order. Chaos, Solitons & Fractals 22 (2004) 443-450
    • (2004) Chaos, Solitons & Fractals , vol.22 , pp. 443-450
    • Li, C.P.1    Peng, G.J.2
  • 24
    • 0036887936 scopus 로고    scopus 로고
    • Chaos, fractional kinetics, and anomalous transport
    • Zaslavsky G.M. Chaos, fractional kinetics, and anomalous transport. Phys Rep 371 (2002) 461-580
    • (2002) Phys Rep , vol.371 , pp. 461-580
    • Zaslavsky, G.M.1
  • 25
    • 19144371559 scopus 로고    scopus 로고
    • Chaotic dynamics and synchronization of fractional-order Arneodo's systems
    • Lu J.G. Chaotic dynamics and synchronization of fractional-order Arneodo's systems. Chaos, Solitons & Fractals 26 (2005) 1125-1133
    • (2005) Chaos, Solitons & Fractals , vol.26 , pp. 1125-1133
    • Lu, J.G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.