The effects of fractional order on a 3-D quadratic autonomous system with four-wing attractor
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Yanxia Sun | Barend Jacobus van Wyk | Zenghui Wang | Guoyuan Qi | B. V. Wyk | Zenghui Wang | Yanxia Sun | Guoyuan Qi | B. J. Wyk
[1] Elena Grigorenko,et al. Erratum: Chaotic Dynamics of the Fractional Lorenz System [Phys. Rev. Lett.91, 034101 (2003)] , 2006 .
[2] Ingve Simonsen,et al. Inverse statistics in economics: the gain–loss asymmetry , 2002 .
[3] H. Srivastava,et al. Theory and Applications of Fractional Differential Equations , 2006 .
[4] I. S. Jesus,et al. Fractional control of heat diffusion systems , 2008 .
[5] P. Arena,et al. Bifurcation and Chaos in Noninteger Order Cellular Neural Networks , 1998 .
[6] I. Podlubny. Fractional differential equations , 1998 .
[7] Ivo Petráš,et al. Chaos in the fractional-order Volta’s system: modeling and simulation , 2009 .
[8] B. Onaral,et al. Linear approximation of transfer function with a pole of fractional power , 1984 .
[9] Mohammad Saleh Tavazoei,et al. Limitations of frequency domain approximation for detecting chaos in fractional order systems , 2008 .
[10] B. Onaral,et al. Fractal system as represented by singularity function , 1992 .
[11] R. Gorenflo,et al. Fractional calculus and continuous-time finance , 2000, cond-mat/0001120.
[12] E. Ahmed,et al. Equilibrium points, stability and numerical solutions of fractional-order predator–prey and rabies models , 2007 .
[13] L. Chua,et al. The double scroll family , 1986 .
[14] N. Laskin. Fractional market dynamics , 2000 .
[15] Chunguang Li,et al. Chaos and hyperchaos in the fractional-order Rössler equations , 2004 .
[16] Weihua Deng,et al. Short memory principle and a predictor-corrector approach for fractional differential equations , 2007 .
[17] R. Bagley,et al. Fractional order state equations for the control of viscoelasticallydamped structures , 1991 .
[18] R. Koeller. Applications of Fractional Calculus to the Theory of Viscoelasticity , 1984 .
[19] D. Kusnezov,et al. Quantum Levy Processes and Fractional Kinetics , 1999, chao-dyn/9901002.
[20] Ahmed S. Elwakil,et al. Fractional-order Wien-bridge oscillator , 2001 .
[21] J. Sprott. Chaos and time-series analysis , 2001 .
[22] Julien Clinton Sprott,et al. Chaos in fractional-order autonomous nonlinear systems , 2003 .
[23] Anthony N. Michel,et al. Stability of viscoelastic control systems , 1987 .
[24] R. Kutner. Stock market context of the Lévy walks with varying velocity , 2002 .
[25] Xinghuo Yu,et al. Design and analysis of multiscroll chaotic attractors from saturated function series , 2004, IEEE Transactions on Circuits and Systems I: Regular Papers.
[26] S. Wiggins. Introduction to Applied Nonlinear Dynamical Systems and Chaos , 1989 .
[27] A. Wolf,et al. Determining Lyapunov exponents from a time series , 1985 .
[28] C. F. Lorenzo,et al. Chaos in a fractional order Chua's system , 1995 .
[29] D. Matignon. Stability results for fractional differential equations with applications to control processing , 1996 .
[30] P. Arena,et al. Chaotic behavior in noninteger-order cellular neural networks , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.
[31] R. Koeller. Polynomial operators, stieltjes convolution, and fractional calculus in hereditary mechanics , 1986 .
[32] Guanrong Chen,et al. A four-wing chaotic attractor generated from a new 3-D quadratic autonomous system , 2008 .
[33] C. P. Silva,et al. Shil'nikov's theorem-a tutorial , 1993 .
[34] M. Haeri,et al. Unreliability of frequency-domain approximation in recognising chaos in fractional-order systems , 2007 .
[35] Elena Grigorenko,et al. Chaotic dynamics of the fractional Lorenz system. , 2003, Physical review letters.
[36] Mohammad Saleh Tavazoei,et al. A necessary condition for double scroll attractor existence in fractional-order systems , 2007 .
[37] Weihua Deng,et al. Numerical algorithm for the time fractional Fokker-Planck equation , 2007, J. Comput. Phys..
[38] A. Darbyshire. Calculating Lyapunov exponents from a time series , 1994 .