Controlling phase multistability in coupled period-doubling oscillators.

A simple method of switching between coexisting attractors in two coupled period-doubling oscillators is proposed. It is based on "pulling" phases of oscillations into suitable value by means of two periodic forces which simultaneously influence the both sub-systems. The frequency and the phase-shift of the forces are key parameters of the control. Their choice determines the resulted regime. The method is tested on example of coupled Chua's oscillators and exhibits its efficiency both for periodic and for chaotic attractors.

[1]  G. Bard Ermentrout,et al.  Phase locking in chains of multiple-coupled oscillators , 2000 .

[2]  V. Astakhov,et al.  Multistability formation and synchronization loss in coupled Hénon maps: two sides of the single bifurcational mechanism. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  Alexander N. Pisarchik,et al.  ATTRACTOR SPLITTING INDUCED BY RESONANT PERTURBATIONS , 1997 .

[4]  Vicente Pérez-Muñuzuri,et al.  Interaction of chaotic rotating waves in coupled rings of chaotic cells , 1999 .

[5]  Foss,et al.  Multistability and delayed recurrent loops. , 1996, Physical review letters.

[6]  Rabinder N Madan,et al.  Chua's Circuit: A Paradigm for Chaos , 1993, Chua's Circuit.

[7]  Ying-Cheng Lai,et al.  Driving trajectories to a desirable attractor by using small control , 1996 .

[8]  V. Pérez-Villar,et al.  Size instabilities in rings of chaotic synchronized systems , 1997 .

[9]  G. Ermentrout The behavior of rings of coupled oscillators , 1985, Journal of mathematical biology.

[10]  DYNAMICS OF TWO COUPLED CHUA'S CIRCUITS , 1995 .

[11]  M. Golubitsky,et al.  Ponies on a merry-go-round in large arrays of Josephson junctions , 1991 .

[12]  F. Arecchi,et al.  Experimental evidence of subharmonic bifurcations, multistability, and turbulence in a Q-switched gas laser , 1982 .

[13]  A N Pisarchik,et al.  Controlling the multistability of nonlinear systems with coexisting attractors. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  Ilʹi︠a︡ Izrailevich Blekhman,et al.  Synchronization in science and technology , 1988 .

[15]  B. Bezruchko,et al.  Oscillation types, multistability, and basins of attractors in symmetrically coupled period-doubling systems , 2003 .

[16]  Goswami,et al.  Annihilation of one of the coexisting attractors in a bistable system , 2000, Physical review letters.

[17]  B. Goswami Control of multistate hopping intermittency. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  T. Vadivasova,et al.  Phase Multistability of Synchronous Chaotic Oscillations , 2000 .

[19]  Tomasz Kapitaniak,et al.  Loss of Chaos Synchronization through the Sequence of Bifurcations of Saddle Periodic Orbits , 1997 .

[20]  Wacker,et al.  Simple model for multistability and domain formation in semiconductor superlattices. , 1994, Physical review. B, Condensed matter.

[21]  L. Chua,et al.  GLOBAL BIFURCATION ANALYSIS OF THE DOUBLE SCROLL CIRCUIT , 1991 .

[22]  G. Ermentrout Stable periodic solutions to discrete and continuum arrays of weakly coupled nonlinear oscillators , 1992 .

[23]  M. Hasler,et al.  Effect of parameter mismatch on the mechanism of chaos synchronization loss in coupled systems , 1998 .

[24]  V. Astakhov,et al.  Phase multistability and phase synchronization in an array of locally coupled period-doubling oscillators. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  Peter Ashwin,et al.  Three identical oscillators with symmetric coupling , 1990 .

[26]  Jürgen Kurths,et al.  Synchronization: Phase locking and frequency entrainment , 2001 .

[27]  Phase Multistability in Coupled Oscillator Systems , 2003 .

[28]  Celso Grebogi,et al.  Driving trajectories in complex systems , 1999 .

[29]  V. Pérez-Villar,et al.  Observation of a Fast Rotating Wave in Rings of Coupled Chaotic Oscillators , 1997 .

[30]  F. Arecchi,et al.  Control of stochastic multistable systems: experimental demonstration. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[31]  T. Antonsen,et al.  Mode switching in a gyrotron with azimuthally corrugated resonator. , 2007 .

[32]  Sun,et al.  Multistability of conductance in doped semiconductor superlattices. , 1995, Physical review. B, Condensed matter.