Transitions to amplitude death in a regular array of nonlinear oscillators.

We investigate amplitude death in a regular array of nonlinear oscillators. We find that the system undergoes three transitions during the road to complete amplitude death. The first two are related to partial amplitude death: one induces partial amplitude death and the other enhances it. The last transition establishes complete amplitude death. We also find that the first two belong to a second-order transition and are universal while the last one is strongly dependent on the system parameters.

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

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

[3]  Thomas Erneux,et al.  LOCALIZED SYNCHRONIZATION IN TWO COUPLED NONIDENTICAL SEMICONDUCTOR LASERS , 1997 .

[4]  I Ozden,et al.  Strong coupling of nonlinear electronic and biological oscillators: reaching the "amplitude death" regime. , 2004, Physical review letters.

[5]  M. Sushchik,et al.  Disorder can eliminate oscillator death , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[6]  F. Atay.  Distributed delays facilitate amplitude death of coupled oscillators. , 2003, Physical review letters.

[7]  Junzhong Yang,et al.  Partial amplitude death in coupled chaotic oscillators. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[9]  M. M. Sushchik,et al.  Patterns in networks of oscillators formed via synchronization and oscillator death , 2002, Math. Comput. Simul..

[10]  G. B. Ermentrout,et al.  The uniqueness and stability of the rest state for strongly coupled oscillators , 1989 .

[11]  Fatihcan M. Atay,et al.  Total and partial amplitude death in networks of diffusively coupled oscillators , 2003 .

[12]  Awadhesh Prasad,et al.  Amplitude death in coupled chaotic oscillators. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  Zhonghuai Hou,et al.  Oscillator death on small-world networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  D. V. Reddy,et al.  Time delay effects on coupled limit cycle oscillators at Hopf bifurcation , 1998, chao-dyn/9810023.

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

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

[17]  Epstein,et al.  Coupled chaotic chemical oscillators. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

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

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

[20]  Fatihcan M. Atay,et al.  Oscillator death in coupled functional differential equations near Hopf bifurcation , 2006 .