메뉴 건너뛰기




Volumn 15, Issue 2, 2010, Pages 384-393

A note on the fractional-order Volta's system

Author keywords

Double scroll attractor; Fractional calculus; Fractional order Volta's system

Indexed keywords

CALCULATIONS;

EID: 69049113859     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2009.04.009     Document Type: Article
Times cited : (47)

References (55)
  • 1
    • 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 8 7 (1998) 1527-1539
    • (1998) Int J Bifurcat Chaos , vol.8 , Issue.7 , pp. 1527-1539
    • Arena, P.1    Caponetto, R.2    Fortuna, L.3    Porto, D.4
  • 3
    • 20444477489 scopus 로고    scopus 로고
    • Hyperchaos in fractional order nonlinear systems
    • Ahmad W.M. Hyperchaos in fractional order nonlinear systems. Chaos Solitons Fract 26 (2005) 1459-1465
    • (2005) Chaos Solitons Fract , vol.26 , pp. 1459-1465
    • Ahmad, W.M.1
  • 4
    • 34748856163 scopus 로고    scopus 로고
    • Analysis of the Van der Pol oscillator containing derivatives of fractional order
    • Barbosa R.S., Tenreiro Machado J.A., Vinagre B.M., and Calderón A.J. Analysis of the Van der Pol oscillator containing derivatives of fractional order. J Vib Control 13 9-10 (2007) 1291-1301
    • (2007) J Vib Control , vol.13 , Issue.9-10 , pp. 1291-1301
    • Barbosa, R.S.1    Tenreiro Machado, J.A.2    Vinagre, B.M.3    Calderón, A.J.4
  • 6
    • 0003956339 scopus 로고
    • Numerical models for simulation the fractional-order control systems, UEF-04-94
    • Institute of Experimental Physics;
    • Dorčák Ľ. Numerical models for simulation the fractional-order control systems, UEF-04-94. Košice, Slovakia: The Academy of Sciences, Institute of Experimental Physics; 1994.
    • (1994) Košice, Slovakia: The Academy of Sciences
    • Dorčák, L.1
  • 7
    • 0026928376 scopus 로고
    • Fractal systems as represented by singularity function
    • Charef A., Sun H.H., Tsao Y.Y., and Onaral G. Fractal systems as represented by singularity function. IEEE Trans Autom Control 37 9 (1992) 1465-1470
    • (1992) IEEE Trans Autom Control , vol.37 , Issue.9 , pp. 1465-1470
    • Charef, A.1    Sun, H.H.2    Tsao, Y.Y.3    Onaral, G.4
  • 8
    • 15544372160 scopus 로고    scopus 로고
    • Continued fraction expansion approaches to discretizing fractional order derivatives - an expository review
    • Chen Y.Q., Vinagre B.M., and Podlubny I. Continued fraction expansion approaches to discretizing fractional order derivatives - an expository review. Nonlinear Dyn 38 1-4 (2004) 155-170
    • (2004) Nonlinear Dyn , vol.38 , Issue.1-4 , pp. 155-170
    • Chen, Y.Q.1    Vinagre, B.M.2    Podlubny, I.3
  • 9
    • 18844427587 scopus 로고    scopus 로고
    • Chaos synchronization of the fractional Lu system
    • Deng W.H., and Li C.P. Chaos synchronization of the fractional Lu system. Phys A 353 (2005) 61-72
    • (2005) Phys A , vol.353 , pp. 61-72
    • Deng, W.H.1    Li, C.P.2
  • 10
    • 34249335010 scopus 로고    scopus 로고
    • Short memory principle and a predictor-corrector approach for fractional differential equations
    • Deng W. Short memory principle and a predictor-corrector approach for fractional differential equations. J Comput Appl Math 206 (2007) 174-188
    • (2007) J Comput Appl Math , vol.206 , pp. 174-188
    • Deng, W.1
  • 11
    • 36149001762 scopus 로고    scopus 로고
    • Numerical algorithm for the time fractional Fokker-Planck equation
    • Deng W. Numerical algorithm for the time fractional Fokker-Planck equation. J Comput Phys 227 (2007) 1510-1522
    • (2007) J Comput Phys , vol.227 , pp. 1510-1522
    • Deng, W.1
  • 12
    • 33947133956 scopus 로고    scopus 로고
    • Stability analysis of linear fractional differential system with multiple time delays
    • Deng W., Li Ch., and Lu J. Stability analysis of linear fractional differential system with multiple time delays. Nonlinear Dyn 48 (2007) 409-416
    • (2007) Nonlinear Dyn , vol.48 , pp. 409-416
    • Deng, W.1    Li, Ch.2    Lu, J.3
  • 13
    • 10644238068 scopus 로고    scopus 로고
    • Algorithms for the fractional calculus: a selection of numerical methods
    • Diethelm K., Ford N.J., Freed A.D., and Luchko Yu. Algorithms for the fractional calculus: a selection of numerical methods. Comput Methods Appl Mech Eng 194 (2005) 743-773
    • (2005) Comput Methods Appl Mech Eng , vol.194 , pp. 743-773
    • Diethelm, K.1    Ford, N.J.2    Freed, A.D.3    Luchko, Yu.4
  • 14
    • 0035625795 scopus 로고    scopus 로고
    • The numerical solution of fractional differential equations: Speed versus accuracy
    • Manchester: Manchester Centre for Computational Mathematics;
    • Ford N, Simpson A. The numerical solution of fractional differential equations: speed versus accuracy. Numerical Analysis Report 385. Manchester: Manchester Centre for Computational Mathematics; 2001.
    • (2001) Numerical Analysis Report , vol.385
    • Ford, N.1    Simpson, A.2
  • 15
    • 12444328794 scopus 로고    scopus 로고
    • Chaos in the fractional order periodically forced complex Duffing's oscillators
    • Gao X., and Yu J. Chaos in the fractional order periodically forced complex Duffing's oscillators. Chaos Solitons Fract 24 (2005) 1097-1104
    • (2005) Chaos Solitons Fract , vol.24 , pp. 1097-1104
    • Gao, X.1    Yu, J.2
  • 18
    • 0036530321 scopus 로고    scopus 로고
    • A note on time-domain simulation of feedback fractional-order systems
    • Hwang Ch., Leu J.F., and Tsay S.Y. A note on time-domain simulation of feedback fractional-order systems. IEEE Trans Autom Control 47 4 (2002) 625-631
    • (2002) IEEE Trans Autom Control , vol.47 , Issue.4 , pp. 625-631
    • Hwang, Ch.1    Leu, J.F.2    Tsay, S.Y.3
  • 19
    • 3342927052 scopus 로고    scopus 로고
    • Chaos and hyperchaos in the fractional-order Rossler equations
    • Li Ch., and Chen G. Chaos and hyperchaos in the fractional-order Rossler equations. Phys A 341 (2004) 55-61
    • (2004) Phys A , vol.341 , pp. 55-61
    • Li, Ch.1    Chen, G.2
  • 21
    • 1842832060 scopus 로고    scopus 로고
    • Chaos in Chen's system with a fractional order
    • Li Ch., and Peng G. Chaos in Chen's system with a fractional order. Chaos Solitons Fract 22 (2004) 443-450
    • (2004) Chaos Solitons Fract , vol.22 , pp. 443-450
    • Li, Ch.1    Peng, G.2
  • 23
    • 23144435914 scopus 로고    scopus 로고
    • A note on the fractional-order Chen system
    • Lu J.G., and Chen G. A note on the fractional-order Chen system. Chaos Solitons Fract 27 (2006) 685-688
    • (2006) Chaos Solitons Fract , vol.27 , pp. 685-688
    • Lu, J.G.1    Chen, G.2
  • 24
    • 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 Fract 26 (2005) 1125-1133
    • (2005) Chaos Solitons Fract , vol.26 , pp. 1125-1133
    • Lu, J.G.1
  • 25
    • 23844464799 scopus 로고    scopus 로고
    • Chaotic dynamics and synchronization of fractional-order Chua's circuits with a piecewise-linear nonlinearity
    • Lu J.G. Chaotic dynamics and synchronization of fractional-order Chua's circuits with a piecewise-linear nonlinearity. Int J Modern Phys B 19 20 (2005) 3249-3259
    • (2005) Int J Modern Phys B , vol.19 , Issue.20 , pp. 3249-3259
    • Lu, J.G.1
  • 27
    • 0002731965 scopus 로고    scopus 로고
    • Stability result on fractional differential equations with applications to control processing
    • Lille, France, July;
    • Matignon D. Stability result on fractional differential equations with applications to control processing. In: IMACS-SMC proceedings, Lille, France, July; 1996. p. 963-8.
    • (1996) IMACS-SMC proceedings , pp. 963-968
    • Matignon, D.1
  • 29
    • 0000196448 scopus 로고
    • Basic characteristics of a fractance device
    • Nakagava M., and Sorimachi K. Basic characteristics of a fractance device. IEICE Trans Fundam E75-A 12 (1992) 1814-1818
    • (1992) IEICE Trans Fundam , vol.E75-A , Issue.12 , pp. 1814-1818
    • Nakagava, M.1    Sorimachi, K.2
  • 30
    • 0002339320 scopus 로고    scopus 로고
    • The effects of continuously varying the fractional differential order of chaotic nonlinear systems
    • Nimmo S., and Evans A.K. The effects of continuously varying the fractional differential order of chaotic nonlinear systems. Chaos Solitons Fract 10 7 (1999) 1111-1118
    • (1999) Chaos Solitons Fract , vol.10 , Issue.7 , pp. 1111-1118
    • Nimmo, S.1    Evans, A.K.2
  • 33
    • 79961019126 scopus 로고    scopus 로고
    • An overview of the CRONE approach in system analysis, modeling and identification, observation and control
    • Seoul, Korea, July 6-11
    • Oustaloup A, Sabatier J, Lanusse P, Malti R, Melchior P, Moreau X, et al. An overview of the CRONE approach in system analysis, modeling and identification, observation and control. In: Proceedings of the 17th World Congress IFAC, Seoul, Korea, July 6-11, 2008. p. 14254-65.
    • (2008) Proceedings of the 17th World Congress IFAC , pp. 14254-14265
    • Oustaloup, A.1    Sabatier, J.2    Lanusse, P.3    Malti, R.4    Melchior, P.5    Moreau, X.6
  • 34
    • 33750492918 scopus 로고    scopus 로고
    • Effective medium equations for fractional Fick's law in porous media
    • Parada F.J.V., Tapia J.A.O., and Ramirez J.A. Effective medium equations for fractional Fick's law in porous media. Phys A 373 (2007) 339-353
    • (2007) Phys A , vol.373 , pp. 339-353
    • Parada, F.J.V.1    Tapia, J.A.O.2    Ramirez, J.A.3
  • 35
    • 23844549787 scopus 로고    scopus 로고
    • Control of fractional-order Chua's system
    • Petráš I. Control of fractional-order Chua's system. J Electr Eng 53 7-8 (2002) 219-222
    • (2002) J Electr Eng , vol.53 , Issue.7-8 , pp. 219-222
    • Petráš, I.1
  • 36
    • 67449143012 scopus 로고    scopus 로고
    • Fractional-order control systems: modelling and simulation
    • Petráš I., and Dorčák L. Fractional-order control systems: modelling and simulation. Fract Calculus Appl Anal 6 2 (2003) 205-232
    • (2003) Fract Calculus Appl Anal , vol.6 , Issue.2 , pp. 205-232
    • Petráš, I.1    Dorčák, L.2
  • 37
    • 67449110445 scopus 로고    scopus 로고
    • Chaos in the fractional-order Volta's system: modeling and simulation
    • 10.1007/s11071-008-9429-0
    • Petráš I. Chaos in the fractional-order Volta's system: modeling and simulation. Nonlinear Dyn (2008) 10.1007/s11071-008-9429-0
    • (2008) Nonlinear Dyn
    • Petráš, I.1
  • 38
    • 41849104190 scopus 로고    scopus 로고
    • A note on the fractional-order Chua's system
    • Petráš I. A note on the fractional-order Chua's system. Chaos Solitons Fract 38 1 (2008) 140-147
    • (2008) Chaos Solitons Fract , vol.38 , Issue.1 , pp. 140-147
    • Petráš, I.1
  • 42
    • 0242354999 scopus 로고    scopus 로고
    • Geometric and physical interpretation of fractional integration and fractional differentiation
    • Podlubny I. Geometric and physical interpretation of fractional integration and fractional differentiation. Fract Calculus Appl Anal 5 4 (2002) 367-386
    • (2002) Fract Calculus Appl Anal , vol.5 , Issue.4 , pp. 367-386
    • Podlubny, I.1
  • 44
    • 33744801528 scopus 로고    scopus 로고
    • Matrix approach to discrete fractional calculus
    • Podlubny I. Matrix approach to discrete fractional calculus. Fract Calculus Appl Anal 3 4 (2000) 359-386
    • (2000) Fract Calculus Appl Anal , vol.3 , Issue.4 , pp. 359-386
    • Podlubny, I.1
  • 45
    • 61349186917 scopus 로고    scopus 로고
    • Matrix approach to discrete fractional calculus. II: Partial fractional differential equations
    • Podlubny I., Chechkin A., Skovranek T., Chen Y.Q., and Vinagre Jara B.M. Matrix approach to discrete fractional calculus. II: Partial fractional differential equations. J Comput Phys 228 8 (2009) 3137-3153
    • (2009) J Comput Phys , vol.228 , Issue.8 , pp. 3137-3153
    • Podlubny, I.1    Chechkin, A.2    Skovranek, T.3    Chen, Y.Q.4    Vinagre Jara, B.M.5
  • 46
    • 0242270972 scopus 로고    scopus 로고
    • Two direct Tustin discretization methods for fractional-order differentiator/integrator
    • Vinagre B.M., Chen Y.Q., and Petráš I. Two direct Tustin discretization methods for fractional-order differentiator/integrator. J Franklin Inst 340 (2003) 349-362
    • (2003) J Franklin Inst , vol.340 , pp. 349-362
    • Vinagre, B.M.1    Chen, Y.Q.2    Petráš, I.3
  • 47
    • 37549042003 scopus 로고    scopus 로고
    • Unreliability of frequency-domain approximation in recognising chaos in fractional-order systems
    • Tavazoei M.S., and Haeri M. Unreliability of frequency-domain approximation in recognising chaos in fractional-order systems. IET Signal Process 1 4 (2007) 171-181
    • (2007) IET Signal Process , vol.1 , Issue.4 , pp. 171-181
    • Tavazoei, M.S.1    Haeri, M.2
  • 48
    • 34347330038 scopus 로고    scopus 로고
    • A necessary condition for double scroll attractor existence in fractional-order systems
    • Tavazoei M.S., and Haeri M. A necessary condition for double scroll attractor existence in fractional-order systems. Phys Lett A 367 (2007) 102-113
    • (2007) Phys Lett A , vol.367 , pp. 102-113
    • Tavazoei, M.S.1    Haeri, M.2
  • 49
    • 44649156296 scopus 로고    scopus 로고
    • Limitations of frequency domain approximation for detecting chaos in fractional order systems
    • Tavazoei M.S., and Haeri M. Limitations of frequency domain approximation for detecting chaos in fractional order systems. Nonlinear Anal 69 (2008) 1299-1320
    • (2008) Nonlinear Anal , vol.69 , pp. 1299-1320
    • Tavazoei, M.S.1    Haeri, M.2
  • 50
    • 51249088596 scopus 로고    scopus 로고
    • Chaotic attractors in incommensurate fractional order systems
    • Tavazoei M.S., and Haeri M. Chaotic attractors in incommensurate fractional order systems. Phys D 237 (2008) 2628-2637
    • (2008) Phys D , vol.237 , pp. 2628-2637
    • Tavazoei, M.S.1    Haeri, M.2
  • 51
    • 0021439912 scopus 로고
    • On the appearance of the fractional derivative in the behavior of real materials
    • Torvik P.J., and Bagley R.L. On the appearance of the fractional derivative in the behavior of real materials. Trans ASME 51 (1984) 294-298
    • (1984) Trans ASME , vol.51 , pp. 294-298
    • Torvik, P.J.1    Bagley, R.L.2
  • 52
    • 33846560756 scopus 로고    scopus 로고
    • Design of FIR and IIR fractional order Simpson digital integrators
    • Tseng Ch.Ch. Design of FIR and IIR fractional order Simpson digital integrators. Signal Process 87 (2007) 1045-1057
    • (2007) Signal Process , vol.87 , pp. 1045-1057
    • Tseng, Ch.Ch.1
  • 53
    • 0023401151 scopus 로고
    • Realizations of generalized Warburg impedance with RC ladder networks and transmission lines
    • Wang J.C. Realizations of generalized Warburg impedance with RC ladder networks and transmission lines. J Electrochem Soc 134 8 (1987) 1915-1920
    • (1987) J Electrochem Soc , vol.134 , Issue.8 , pp. 1915-1920
    • Wang, J.C.1
  • 55
    • 0008494528 scopus 로고
    • Determining Lyapunov exponents from a time series
    • Wolf A., Swift J.B., Swinney H.L., and Vastano J.A. Determining Lyapunov exponents from a time series. Phys D 16 (1985) 285-317
    • (1985) Phys D , vol.16 , pp. 285-317
    • Wolf, A.1    Swift, J.B.2    Swinney, H.L.3    Vastano, J.A.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.