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Volumn 20, Issue 3, 2010, Pages 669-678

An effective method for detecting chaos in fractional-order systems

Author keywords

Adomian decomposition method; Binary test for detecting fractional chaos; Fractional order Chen system; Fractional order Chua's circuit; Fractional order Lorenz system; Fractional order systems

Indexed keywords

ALGEBRA; BINS; DIFFERENTIAL EQUATIONS; DYNAMICAL SYSTEMS; PHASE SPACE METHODS; RANDOM PROCESSES;

EID: 77951925589     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127410025958     Document Type: Conference Paper
Times cited : (31)

References (45)
  • 3
    • 0037332868 scopus 로고    scopus 로고
    • Chaos in fractional-order autonomous nonlinear systems
    • Ahmad, W. M. & Sprott, J. C. [2003] "Chaos in fractional-order autonomous nonlinear systems," Chaos Solit. Fract. 16, 339-351.
    • (2003) Chaos Solit. Fract. , vol.16 , pp. 339-351
    • Ahmad, W.M.1    Sprott, J.C.2
  • 5
    • 27844563993 scopus 로고    scopus 로고
    • Subexponential decay of correlations for compact group extensions of nonuniformly expanding systems
    • Bruin, H., Holland, M. & Melbourne, I. [2005] "Subexponential decay of correlations for compact group extensions of nonuniformly expanding systems," Ergod. Th. Dyn. Syst. 25, 1719-1738.
    • (2005) Ergod. Th. Dyn. Syst. , vol.25 , pp. 1719-1738
    • Bruin, H.1    Holland, M.2    Melbourne, I.3
  • 7
    • 36348976811 scopus 로고    scopus 로고
    • Fractional calculus: A mathematical tool from the past for present engineers
    • Cafagna, D. [2007] "Fractional calculus: A mathematical tool from the past for present engineers," IEEE Ind. Electron. Mag. 1, 35-40.
    • (2007) IEEE Ind. Electron. Mag. , vol.1 , pp. 35-40
    • Cafagna, D.1
  • 8
    • 33947709419 scopus 로고    scopus 로고
    • Decomposition method for studying smooth Chuas equation with application to hyperchaotic multi-scroll attractors
    • Cafagna, D. & Grassi, G. [2007] "Decomposition method for studying smooth Chuas equation with application to hyperchaotic multi-scroll attractors," Int. J. Bifurcation and Chaos 17, 209-226.
    • (2007) Int. J. Bifurcation and Chaos , vol.17 , pp. 209-226
    • Cafagna, D.1    Grassi, G.2
  • 9
    • 45149102412 scopus 로고    scopus 로고
    • Fractional-order Chuas circuit: Time-domain analysis, bifurcation, chaotic behavior and test for chaos
    • Cafagna, D. & Grassi, G. [2008a] "Fractional-order Chuas circuit: Time-domain analysis, bifurcation, chaotic behavior and test for chaos," Int. J. Bifurcation and Chaos 18, 615-639.
    • (2008) Int. J. Bifurcation and Chaos , vol.18 , pp. 615-639
    • Cafagna, D.1    Grassi, G.2
  • 10
    • 52149110344 scopus 로고    scopus 로고
    • Bifurcation and chaos in the fractional-order Chen system via a time-domain approach
    • Cafagna, D. & Grassi, G. [2008b] "Bifurcation and chaos in the fractional-order Chen system via a time-domain approach," Int. J. Bifurcation and Chaos 18, 1845-1863.
    • (2008) Int. J. Bifurcation and Chaos , vol.18 , pp. 1845-1863
    • Cafagna, D.1    Grassi, G.2
  • 11
    • 84977255207 scopus 로고
    • Linear models of dissipation whose Q is almost frequency independent. Part II
    • Caputo, M. [1967] "Linear models of dissipation whose Q is almost frequency independent. Part II," J. Roy. Astr. Soc. 13, 529-539.
    • (1967) J. Roy. Astr. Soc. , vol.13 , pp. 529-539
    • Caputo, M.1
  • 12
    • 44949273552 scopus 로고
    • State space reconstruction in the presence of noise
    • Casdagli, M., Eubank, S., Farmer, J. D. & Gibson, J. [1991] "State space reconstruction in the presence of noise," Physica D 51, 52-98.
    • (1991) Physica D , vol.51 , pp. 52-98
    • Casdagli, M.1    Eubank, S.2    Farmer, J.D.3    Gibson, J.4
  • 13
    • 0026928376 scopus 로고
    • Fractal systems as represented by singularity function
    • Charef, A., Sun, H., Tsao, B. & Onaral, B. [1992] "Fractal systems as represented by singularity function," IEEE Trans. Autom. Cont. 37, 1465-1470.
    • (1992) IEEE Trans. Autom. Cont. , vol.37 , pp. 1465-1470
    • Charef, A.1    Sun, H.2    Tsao, B.3    Onaral, B.4
  • 15
    • 34548530905 scopus 로고    scopus 로고
    • Chaotic dynamics of the fractionally damped van der Pol equation
    • Chen, J. H. & Chen, W. C. [2008] "Chaotic dynamics of the fractionally damped van der Pol equation," Chaos Solit. Fract. 35, 188-198.
    • (2008) Chaos Solit. Fract. , vol.35 , pp. 188-198
    • Chen, J.H.1    Chen, W.C.2
  • 16
    • 10344238128 scopus 로고    scopus 로고
    • Adomian decomposition: A tool for solving a system of fractional differential equations
    • DOI 10.1016/j.jmaa.2004.07.039, PII S0022247X04006286
    • Daftardar-Gejji, V. & Jafari, H. [2005] "Adomian decomposition: A tool for solving a system of fractional differential equations," J. Math. Anal. Appl. 301, 508-518. (Pubitemid 39630973)
    • (2005) Journal of Mathematical Analysis and Applications , vol.301 , Issue.2 , pp. 508-518
    • Daftardar-Gejji, V.1    Jafari, H.2
  • 17
    • 37549047625 scopus 로고    scopus 로고
    • The evolution of chaotic dynamics for fractional unified system
    • Deng, W. & Li, C. P. [2008] "The evolution of chaotic dynamics for fractional unified system," Phys. Lett. A 372, 401-407.
    • (2008) Phys. Lett. A , vol.372 , pp. 401-407
    • Deng, W.1    Li, C.P.2
  • 18
    • 0036650479 scopus 로고    scopus 로고
    • A predictor-corrector approach for the numerical solution of fractional differential equations
    • Diethelm, K., Ford, N. J. & Freed, A. D. [2002] "A predictor-corrector approach for the numerical solution of fractional differential equations," Nonlin. Dyn. 29, 3-22.
    • (2002) Nonlin. Dyn. , vol.29 , pp. 3-22
    • Diethelm, K.1    Ford, N.J.2    Freed, A.D.3
  • 20
    • 0037331481 scopus 로고    scopus 로고
    • Decay of correlations, central limit theorems and approximations by Brownian motion for compact Lie group extensions
    • Field, M., Melbourne, I. & Török, A. [2003] "Decay of correlations, central limit theorems and approximations by Brownian motion for compact Lie group extensions," Ergod. Th. Dyn. Syst. 23, 87-110.
    • (2003) Ergod. Th. Dyn. Syst. , vol.23 , pp. 87-110
    • Field, M.1    Melbourne, I.2    Török, A.3
  • 21
    • 0002847893 scopus 로고    scopus 로고
    • Fractional calculus: Integral and differential equations of fractional order
    • (Springer-Verlag, Wien)
    • Gorenflo, R. & Mainardi, F. [1997] "Fractional calculus: Integral and differential equations of fractional order," in Fractal and Fractional Calculus in Continuum Mechanics (Springer-Verlag, Wien), pp. 223-276.
    • (1997) Fractal and Fractional Calculus in Continuum Mechanics , pp. 223-276
    • Gorenflo, R.1    Mainardi, F.2
  • 22
    • 1542512469 scopus 로고    scopus 로고
    • A new test for chaos in deterministic systems
    • Gottwald, G. A. & Melbourne, I. [2004] "A new test for chaos in deterministic systems," Proc. R. Soc. Lond. A 460, 603-611.
    • (2004) Proc. R. Soc. Lond. A , vol.460 , pp. 603-611
    • Gottwald, G.A.1    Melbourne, I.2
  • 23
    • 27744608106 scopus 로고    scopus 로고
    • Testing for chaos in deterministic systems with noise
    • Gottwald, G. A. & Melbourne, I. [2005] "Testing for chaos in deterministic systems with noise," Physica D 212, 100-110.
    • (2005) Physica D , vol.212 , pp. 100-110
    • Gottwald, G.A.1    Melbourne, I.2
  • 24
    • 0041384356 scopus 로고    scopus 로고
    • Chaotic dynamics of the fractional Lorenz system
    • Grigorenko, I. & Grigorenko, E. [2003] "Chaotic dynamics of the fractional Lorenz system," Phys. Rev. Lett. 91, 34101-34104.
    • (2003) Phys. Rev. Lett. , vol.91 , pp. 34101-34104
    • Grigorenko, I.1    Grigorenko, E.2
  • 29
    • 3342927052 scopus 로고    scopus 로고
    • Chaos and hyperchaos in the fractional-order Rössler equations
    • Li, C. G. & Chen, G. R. [2004a] "Chaos and hyperchaos in the fractional-order Rössler equations," Phys. A 341, 55-61.
    • (2004) Phys. A , vol.341 , pp. 55-61
    • Li, C.G.1    Chen, G.R.2
  • 30
    • 2042470796 scopus 로고    scopus 로고
    • Chaos in the fractionalorder Chen system and its control
    • Li, C. G. & Chen, G. [2004b] "Chaos in the fractionalorder Chen system and its control," Chaos Solit. Fract. 22, 549-554.
    • (2004) Chaos Solit. Fract. , vol.22 , pp. 549-554
    • Li, C.G.1    Chen, G.2
  • 31
    • 27744554781 scopus 로고    scopus 로고
    • Chaos synchronization of the Chua system with a fractional order
    • Li, C. P., Deng, W. H. & Xu, D. [2006] "Chaos synchronization of the Chua system with a fractional order," Physica A 360, 171-185.
    • (2006) Physica A , vol.360 , pp. 171-185
    • Li, C.P.1    Deng, W.H.2    Xu, D.3
  • 32
    • 0000241853 scopus 로고
    • Deterministic nonperiodic flow
    • Lorenz, E. N. [1963] "Deterministic nonperiodic flow," J. Atmos. Sci. 20, 130-141.
    • (1963) J. Atmos. Sci. , vol.20 , pp. 130-141
    • Lorenz, E.N.1
  • 33
    • 19144371559 scopus 로고    scopus 로고
    • Chaotic dynamics and synchronization of fractional-order Arneodos systems
    • Lu, J. G. [2005] "Chaotic dynamics and synchronization of fractional-order Arneodos systems," Chaos Solit. Fract. 26, 1125-1133.
    • (2005) Chaos Solit. Fract. , vol.26 , pp. 1125-1133
    • Lu, J.G.1
  • 34
    • 33646366905 scopus 로고    scopus 로고
    • Chaotic dynamics of the fractionalorder Lu system and its synchronization
    • Lu, J. G. [2006] "Chaotic dynamics of the fractionalorder Lu system and its synchronization," Phys. Lett. A 354, 305-311.
    • (2006) Phys. Lett. A , vol.354 , pp. 305-311
    • Lu, J.G.1
  • 35
    • 23144435914 scopus 로고    scopus 로고
    • A note on the fractionalorder Chen system
    • Lu, J. G. & Chen, G. [2006] "A note on the fractionalorder Chen system," Chaos Solit. Fract. 27, 685-688.
    • (2006) Chaos Solit. Fract. , vol.27 , pp. 685-688
    • Lu, J.G.1    Chen, G.2
  • 36
    • 34250012626 scopus 로고    scopus 로고
    • Realization of fractionalorder Liu chaotic system by circuit
    • Lu, J. J. & Liu, C. X. [2007] "Realization of fractionalorder Liu chaotic system by circuit," Chinese Phys. 16, 1586-1590.
    • (2007) Chinese Phys , vol.16 , pp. 1586-1590
    • Lu, J.J.1    Liu, C.X.2
  • 37
    • 7544226129 scopus 로고    scopus 로고
    • Statistical properties of endomorphisms and compact group extensions
    • Melbourne, I. & Nicol, M. [2004] "Statistical properties of endomorphisms and compact group extensions," Proc. Lond. Math. Soc. 70, 427-446.
    • (2004) Proc. Lond. Math. Soc. , vol.70 , pp. 427-446
    • Melbourne, I.1    Nicol, M.2
  • 39
    • 0035290132 scopus 로고    scopus 로고
    • Euclidean extensions of dynamical systems
    • Nicol, M., Melbourne, I. & Ashwin, P. [2001] "Euclidean extensions of dynamical systems," Nonlinearity 14, 275-300.
    • (2001) Nonlinearity , vol.14 , pp. 275-300
    • Nicol, M.1    Melbourne, I.2    Ashwin, P.3
  • 43
    • 0021424253 scopus 로고
    • Linear approximation for transfer function with a pole of fractional order
    • Sun, H., Abdelwahed, A. & Onaral, B. [1984] "Linear approximation for transfer function with a pole of fractional order," IEEE Trans. Autom. Cont. 29, 441-444.
    • (1984) IEEE Trans. Autom. Cont. , vol.29 , pp. 441-444
    • Sun, H.1    Abdelwahed, A.2    Onaral, B.3
  • 44
    • 0000779360 scopus 로고
    • Lecture Notes in Mathematics, (Springer, Berlin)
    • Takens, F. [1981] Detecting Strange Attractors in Turbulence, Lecture Notes in Mathematics, Vol.98 (Springer, Berlin), pp. 366-381.
    • (1981) Detecting Strange Attractors in Turbulence , vol.98 , pp. 366-381
    • Takens, F.1
  • 45
    • 22544474192 scopus 로고    scopus 로고
    • Hyperchaos in the fractional-order nonautonomous Chen system and its synchronization
    • Zhang, H. B., Li, C. & Chen, G. [2005] "Hyperchaos in the fractional-order nonautonomous Chen system and its synchronization," Int. J. Mod. Phys. C 16, 1-12.
    • (2005) Int. J. Mod. Phys. C , vol.16 , pp. 1-12
    • Zhang, H.B.1    Li, C.2    Chen, G.3


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