A note on the fractional-order Chua’s system

Abstract This paper deals with fractional-order Chua’s system. It is based on the well-known concept of the Chua’s oscillator, where mathematical model of the Chua’s system consists the fractional-order derivatives. We present the method to derive such kind of the fractional-order model. The fractional-order Chua’s system with a total order less than three, which exhibits chaos as well as other nonlinear behavior, is presented. Numerical experimental example and real measurement are shown to verify the theoretical results.

[1]  Philippe Deregel.  Chua's oscillator: a Zoo of attractors , 1993, J. Circuits Syst. Comput..

[2]  P. Arena,et al.  Bifurcation and Chaos in Noninteger Order Cellular Neural Networks , 1998 .

[3]  K. Moore,et al.  Discretization schemes for fractional-order differentiators and integrators , 2002 .

[4]  Jun-Guo Lu,et al.  Chaotic dynamics and synchronization of fractional-order Arneodo’s systems , 2005 .

[5]  Yangquan Chen,et al.  Two direct Tustin discretization methods for fractional-order differentiator/integrator , 2003, J. Frankl. Inst..

[6]  J. C. Wang.  Realizations of Generalized Warburg Impedance with RC Ladder Networks and Transmission Lines , 1987 .

[7]  Takashi Matsumoto,et al.  A chaotic attractor from Chua's circuit , 1984 .

[8]  S. Westerlund.  Dead matter has memory , 1991 .

[9]  I. Podlubny,et al.  Analogue Realizations of Fractional-Order Controllers , 2002 .

[10]  Changpin Li,et al.  Chaos in Chen's system with a fractional order , 2004 .

[11]  Ivo Petrás,et al.  A Note on the Fractional-Order Cellular Neural Networks , 2006, The 2006 IEEE International Joint Conference on Neural Network Proceedings.

[12]  Chunguang Li,et al.  Chaos and hyperchaos in the fractional-order Rössler equations , 2004 .

[13]  B. Onaral,et al.  Fractal system as represented by singularity function , 1992 .

[14]  S. Westerlund,et al.  Capacitor theory , 1994 .

[15]  P. Arena,et al.  Nonlinear Noninteger Order Circuits and Systems — An Introduction , 2000 .

[16]  Michael Peter Kennedy,et al.  Robust OP Amp Realization of Chua's Circuit , 1992 .

[17]  W. Deng,et al.  Chaos synchronization of the fractional Lü system , 2005 .

[18]  Chyi Hwang,et al.  A note on time-domain simulation of feedback fractional-order systems , 2002, IEEE Trans. Autom. Control..

[19]  Junguo Lu,et al.  CHAOTIC DYNAMICS AND SYNCHRONIZATION OF FRACTIONAL-ORDER CHUA'S CIRCUITS WITH A PIECEWISE-LINEAR NONLINEARITY , 2005 .

[20]  M. Nakagawa,et al.  Basic Characteristics of a Fractance Device , 1992 .

[21]  Wajdi M. Ahmad.  Hyperchaos in fractional order nonlinear systems , 2005 .

[22]  C. F. Lorenzo,et al.  Chaos in a fractional order Chua's system , 1995 .

[23]  Allan K. Evans,et al.  The Effects of Continuously Varying the Fractional Differential Order of Chaotic Nonlinear Systems , 1999 .

[24]  I. Petráš.  Control of Fractional-Order Chua's System , 2000, nlin/0008029.

[25]  Guanrong Chen,et al.  A note on the fractional-order Chen system , 2006 .

[26]  C. Halijak,et al.  Approximation of Fractional Capacitors (1/s)^(1/n) by a Regular Newton Process , 1964 .

[27]  Juebang Yu,et al.  Chaos in the fractional order periodically forced complex Duffing’s oscillators , 2005 .