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Circuit Implementations, Bifurcations and Chaos of a Novel Fractional-Order Dynamical System |
| MIN Fu-Hong**, SHAO Shu-Yi, HUANG Wen-Di, WANG En-Rong |
School of Electrical and Automation Engineering, Nanjing Normal University, Nanjing 210042
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MIN Fu-Hong, SHAO Shu-Yi, HUANG Wen-Di et al 2015 Chin. Phys. Lett. 32 030503 |
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Abstract Linear transfer function approximations of the fractional integrators 1/sm with m=0.80–0.99 with steps of 0.01 are calculated systemically from the fractional order calculus and frequency?domain approximation method. To illustrate the effectiveness for fractional functions, the magnitude Bode diagrams of the actual and approximate transfer functions 1/sm with a slope of -20m dB/decade are depicted. By using the transfer function approximations of the fractional integrators, a new fractional-order nonlinear system is investigated through the bifurcation diagram and Lyapunov exponent. The corresponding circuit of the fractional-order system is designed and the experimental results match perfectly with the numerical simulations.
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Published: 26 February 2015
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[1] Ivo P 2011 Fractional-order Nonlinear Systems Modeling, Analysis and Simulation (Beijing: Higher Education Press)
[2] Hartley T T, Lorenzo C F and Qammer H K 1995 IEEE Trans. Circuits Syst. 42 485
[3] Ahmad W M and Sprott J C 2003 Chaos Solitons Fractals 16 339
[4] Grigorenko I and Grigorenko E 2003 Phys. Rev. Lett. 91 034101
[5] Li C G and Chen G R 2004 Physica A 341 55
[6] Lu J G 2006 Chin. Phys. 15 0301
[7] Han Q, Liu C X, Sun L and Zhu D R 2013 Chin. Phys. B 22 020502
[8] Sun K H, Wang X and Sprott J C 2010 Int. J. Bifurcation Chaos Appl. Sci. Eng. 20 1209
[9] Letellier C and Aguirre L A 2013 Phys. Lett. A 377 1707
[10] Yang N N and Liu C X 2013 Nonlinear Dyn. 74 721
[11] Zhou P and Kuang F 2010 Acta Phys. Sin. 59 6981 (in Chinese)
[12] Shao S Y, Min F H, Ma M L and Wang E R 2013 Acta Phys. Sin. 62 130504 (in Chinese)
[13] Wang L M, Tang Y G, Chai Y Q and Wu F 2014 Chin. Phys. B 23 100501
[14] Xu Z, Liu C X and Yang T 2010 Acta Phys. Sin. 59 1524 (in Chinese)
[15] Li H Q, Liao X F and Luo M W 2012 Nonlinear Dyn. 68 137
[16] Charef A, Sun H H, Tsao Y Y and Onaral B 1992 IEEE Trans. Autom. Control 37 1465 |
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