ESTRUCTURA DEL ESPACIO DE PARÁMETROS PARA LAS ECUACIONES DEL CIRCUITO DE CHUA

We study in detail the parameter space for nonlinear differential equations corresponding to the Chua’s circuit. Our analysis of two and three parameters confirms preliminary results obtained in [1]. In addition, it shows the existence of structures denoting periodicities called “shrimps” and a hub which organizes these structuresinto “spirals”.

[1]  T. Tél,et al.  Chaotic Dynamics: An Introduction Based on Classical Mechanics , 2006 .

[2]  J. Gallas,et al.  Periodicity hub and nested spirals in the phase diagram of a simple resistive circuit. , 2008, Physical review letters.

[3]  D. Watts The “New” Science of Networks , 2004 .

[4]  E. Lorenz Deterministic nonperiodic flow , 1963 .

[5]  Cristian Bonatto,et al.  Self-similarities in the frequency-amplitude space of a loss-modulated CO2 laser. , 2005, Physical review letters.

[6]  L. Chua,et al.  Devil's staircase route to chaos in a non-linear circuit , 1986 .

[7]  Jose Antonio Coarasa Perez,et al.  Evidence for universal chaotic behavior of a driven nonlinear oscillator , 1982 .

[8]  G. Zhong Implementation of Chua's circuit with a cubic nonlinearity , 1994 .

[9]  Yoshisuke Ueda,et al.  Chaotic phase similarities and recurrences in a damped-driven Duffing oscillator. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  J. Sprott Chaos and time-series analysis , 2001 .

[11]  J. Gallas,et al.  Structure of the parameter space of the Hénon map. , 1993, Physical review letters.

[12]  J. Gallas,et al.  Accumulation horizons and period adding in optically injected semiconductor lasers. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  Akio Tsuneda,et al.  A Gallery of attractors from Smooth Chua's equation , 2005, Int. J. Bifurc. Chaos.

[14]  Toshimichi Saito,et al.  Rigorous analyses of windows in a symmetric circuit , 1989, IEEE International Symposium on Circuits and Systems,.

[15]  Leon O. Chua,et al.  Simplest chaotic nonautonomous circuit , 1984 .

[16]  David Aubin,et al.  Writing the History of Dynamical Systems and Chaos: Longue Durée and Revolution, Disciplines and Cultures , 2002 .

[17]  Julien Clinton Sprott,et al.  A new class of chaotic circuit , 2000 .

[18]  Jason A. C. Gallas,et al.  Dissecting shrimps: results for some one-dimensional physical models , 1994 .

[19]  Edward Rietman,et al.  Creating artificial life: self organization , 1993 .

[20]  Albert-László Barabási,et al.  Linked: The New Science of Networks , 2002 .