Oscillation death in coupled nonautonomous systems with parametrical modulation

The oscillation death phenomenon in coupled nonautonomous systems with parametrical excitation has been theoretically identified with two coupled Duffing oscillators. A relation of the death effect with the Hopf bifurcation of the whole system and crisis of coexisting attractors are demonstrated. A parametric linear stability analysis has been performed and compared with results of numerical simulations.

[1]  Alexander N. Pisarchik,et al.  Control of multistability in a directly modulated diode laser , 2002 .

[2]  G. Ermentrout.  Oscillator death in populations of “all to all” coupled nonlinear oscillators , 1990 .

[3]  Kurths,et al.  Phase synchronization of chaotic oscillators. , 1996, Physical review letters.

[4]  Carroll,et al.  Synchronization in chaotic systems. , 1990, Physical review letters.

[5]  Steven H. Strogatz,et al.  Nonlinear dynamics: Death by delay , 1998, Nature.

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

[7]  D. V. Reddy,et al.  Experimental Evidence of Time Delay Induced Death in Coupled Limit Cycle Oscillators , 2000 .

[8]  Alexander N. Pisarchik.  Dynamical tracking of unstable periodic orbits , 1998 .

[9]  Pi,et al.  Experimental observation of the amplitude death effect in two coupled nonlinear oscillators , 2000, Physical review letters.

[10]  G. Ermentrout,et al.  Amplitude response of coupled oscillators , 1990 .

[11]  A N Pisarchik,et al.  Synchronization effects in a dual-wavelength class-B laser with modulated losses. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  Mori,et al.  Coupling among three chemical oscillators: Synchronization, phase death, and frustration. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[13]  Alexander N. Pisarchik,et al.  Shift of critical points in the parametrically modulated Hénon map with coexisting attractors , 2002 .

[14]  Jürgen Kurths,et al.  Synchronization - A Universal Concept in Nonlinear Sciences , 2001, Cambridge Nonlinear Science Series.

[15]  Alexander N. Pisarchik,et al.  Shift of attractor boundaries in systems with a slow harmonic parameter perturbation , 2001 .

[16]  Huw G. Davies,et al.  A period–doubling bifurcation with slow parametric variation and additive noise , 2001, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[17]  S. Strogatz,et al.  Phase diagram for the collective behavior of limit-cycle oscillators. , 1990, Physical review letters.

[18]  Gou,et al.  Persistent properties of crises in a Duffing oscillator. , 1987, Physical review. A, General physics.

[19]  L. Tsimring,et al.  Generalized synchronization of chaos in directionally coupled chaotic systems. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[20]  Michael F. Crowley,et al.  Experimental and theoretical studies of a coupled chemical oscillator: phase death, multistability, and in-phase and out-of-phase entrainment , 1989 .

[21]  H. Fujisaka,et al.  Stability Theory of Synchronized Motion in Coupled-Oscillator Systems , 1983 .

[22]  Arkady Pikovsky,et al.  On the interaction of strange attractors , 1984 .

[23]  J. Kurths,et al.  From Phase to Lag Synchronization in Coupled Chaotic Oscillators , 1997 .

[24]  Sen,et al.  Experimental evidence of time-delay-induced death in coupled limit-cycle oscillators , 1998, Physical review letters.

[25]  S. Strogatz,et al.  Amplitude death in an array of limit-cycle oscillators , 1990 .

[26]  K. Bar-Eli,et al.  On the stability of coupled chemical oscillators , 1985 .

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