İhsan PEHLİVAN, Chunbiao LI, Julien Clinton SPROTT

Amplitude-phase control of a novel chaotic attractor

A novel chaotic attractor with a fractal wing structure is proposed and analyzed in terms of its basic dynamical properties. The most interesting feature of this system is that it has complex dynamical behavior, especially coexisting attractors for particular ranges of the parameters, including two coexisting periodic or strange attractors that can coexist with a third strange attractor. Amplitude and phase control methods are described since they are convenient for circuit design and chaotic signal applications. An appropriately chosen parameter in a particular quadratic coefficient can realize partial amplitude control. An added linear term can change the symmetry and provide an accessible knob to control the phase polarity. Finally, an amplitude-phase controllable circuit is designed using PSpice, and it shows good agreement with the theoretical analysis.

PDF

___

[1] Ozo˘guz S, Elwakil AS, Kennedy MP. Experimental verification of the butterfly attractor in a modified Lorenz ¨ system. Int J Bifur Chaos 2002; 12: 16271632.
[2] Liu X. A new 3D four-wing chaotic system with cubic nonlinearity and its circuit implementation. Chin Phys Lett 2009; 26: 090504.
[3] Dong E, Chen Z, Chen Z, Yuan Z. A novel four-wing chaotic attractor generated from a three-dimensional quadratic autonomous system. Chin Phys B 2009; 18: 26802689.
[4] Qi G, Chen G, Li S, Zhang Y. Four-wing attractors: from pseudo to real. Int J Bifur Chaos 2006; 16: 859885.
[5] Cang S, Qi G. A four-wing-hyper-chaotic attractor and transient chaos generated from a new 4-D quadratic autonomous system. Nonlinear Dynam 2010; 46: 263270.
[6] Elwakil AS, Ozo˘guz S, Kennedy MP. A four-wing butterfly attractor from a fully-autonomous system. Int J Bifur ¨ Chaos 2003; 13: 30933098.
[7] Elwakil AS, Ozo˘guz S, Kennedy MP. Creation of a complex butterfly attractor using a novel Lorenz-type system. ¨ IEEE T Circuits-I 2002; 49: 527530.
[8] Yu S, Lu J, Chen G, Yu X. Design and implementation of grid multiwing butterfly chaotic attractors from a piecewise Lorenz system. IEEE T Circuits-II 2010; 57: 803807.
[9] Yu S, Lu J, Yu X, Chen G. Design and implementation of grid multi-wing hyperchaotic Lorenz system family via switching control and constructing super-heteroclinic loops. IEEE T Circuits-I 2012; 59: 10151028.
[10] Yu S, Lu J, Chen G, Yu X. Generating grid multiwing chaotic attractors by constructing heteroclinic loops into switching systems. IEEE T Circuits-II 2011; 58: 314318.
[11] Elwakil AS, Ozo˘guz S. A system and a circuit for generating multi-butterflies. Int J Bifur Chaos 2008; 18: 841845. ¨
[12] Sprott C, Wang X, Chen G. Coexistence of point, periodic and strange attractors. Int J Bifur Chaos 2013; 23: 1350093.
[13] Qu S, Lu Y, Zhang L, He D. Discontinuous bifurcation and coexistence of attractors in a piecewise linear map with a gap. Chinese Phys B 2008; 17: 4418.
[14] Pehlivan ˙I, Uyaro˘glu Y. Simplified chaotic diffusionless Lorenz attractor and its application to secure communication systems. IET Commun 2007; 1: 10151022.
[15] Pehlivan ˙I, Uyaro˘glu Y. A new chaotic attractor from general Lorenz system family and its electronic experimental implementation. Turk J Electr Eng Co 2010; 18: 171184.
[16] Sundarapandian V, Pehlivan I. Analysis, control, synchronization and circuit design of a novel chaotic system. Math Comput Model 2012; 55: 19041915.
[17] Boccaletti S, Kurths J, Osipov G, Valladares DL, Zhou C. The synchronization of chaotic systems. Phys Rep 2002; 366: 1101.
[18] Lu J, Yu X, Chen G. Chaos synchronization of general complex dynamical networks. Physica A 2004; 334: 281302.
[19] Li C, Chen S, Zhu H. Circuit implementation and synchronization of an improved system with invariable Lyapunov exponent spectrum. Acta Phys Sin 2009; 58: 2255 2265.
[20] Li C, Wang H. An extension system with constant Lyapunov exponent spectrum and its evolvement study. Acta Phys Sin 2009; 58: 75147524.
[21] Li C, Wang J, Hu W. Absolute term introduced to rebuild the chaotic attractor with constant Lyapunov exponent spectrum. Nonlinear Dynam 2012; 68: 575587.
[22] Liu W, Chen G. A new chaotic system and its generation. Int J Bifur Chaos 2003; 13: 261 267.