Time delay effects on coupled limit cycle oscillators at Hopf bifurcation

[1]  N. Minorsky Self‐Excited Mechanical Oscillations , 1948 .

[2]  Y. Aizawa Synergetic Approach to the Phenomena of Mode-Locking in Nonlinear Systems , 1976 .

[3]  M. Kawato,et al.  Two coupled neural oscillators as a model of the circadian pacemaker. , 1980, Journal of theoretical biology.

[4]  A. Winfree The geometry of biological time , 1991 .

[5]  I. Schreiber,et al.  Strange attractors in coupled reaction-diffusion cells , 1982 .

[6]  Yoshiki Kuramoto,et al.  Cooperative Dynamics of Oscillator Community : A Study Based on Lattice of Rings , 1984 .

[7]  Yoshiki Kuramoto,et al.  Chemical Oscillations, Waves, and Turbulence , 1984, Springer Series in Synergetics.

[8]  Alex Zettl,et al.  Charge density wave conduction: A novel collective transport phenomenon in solids , 1985 .

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

[10]  Delisle,et al.  Second-order differential-delay equation to describe a hybrid bistable device. , 1987, Physical review. A, General physics.

[11]  Y. Kuramoto,et al.  Statistical macrodynamics of large dynamical systems. Case of a phase transition in oscillator communities , 1987 .

[12]  Hadley,et al.  Phase locking of Josephson-junction series arrays. , 1988, Physical review. B, Condensed matter.

[13]  Kurt Wiesenfeld,et al.  Phase locking of Josephson junction arrays , 1988 .

[14]  H. Schuster,et al.  Mutual Entrainment of Two Limit Cycle Oscillators with Time Delayed Coupling , 1989 .

[15]  Smith,et al.  Phase locking of relativistic magnetrons. , 1989, Physical review letters.

[16]  K. Satoh Computer Experiment on the Cooperative Behavior of a Network of Interacting Nonlinear Oscillators , 1989 .

[17]  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 .

[18]  M. Shiino,et al.  Synchronization of infinitely many coupled limit-cycle type oscillators , 1989 .

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

[20]  H. Daido,et al.  Intrinsic fluctuations and a phase transition in a class of large populations of interacting oscillators , 1990 .

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

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

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

[24]  Schuster,et al.  Collective frequencies and metastability in networks of limit-cycle oscillators with time delay. , 1991, Physical review letters.

[25]  S. Strogatz,et al.  Dynamics of a large system of coupled nonlinear oscillators , 1991 .

[26]  McKay,et al.  Chaos due to homoclinic and heteroclinic orbits in two coupled oscillators with nonisochronism. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[27]  Munakata,et al.  Clustering behavior of time-delayed nearest-neighbor coupled oscillators. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[28]  Ernst,et al.  Synchronization induced by temporal delays in pulse-coupled oscillators. , 1995, Physical review letters.

[29]  Wiesenfeld,et al.  Synchronization transitions in a disordered Josephson series array. , 1996, Physical review letters.

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

[31]  Wille,et al.  Phase transitions in nonlinear oscillator chains. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[32]  Daido,et al.  Multibranch Entrainment and Scaling in Large Populations of Coupled Oscillators. , 1996, Physical review letters.

[33]  An Experimental Study of a Population of Relaxation Oscillators With a Phase-Repelling Mean-Field Coupling , 1996 .

[34]  H. Daido Onset of cooperative entrainment in limit-cycle oscillators with uniform all-to-all interactions: bifurcation of the order function , 1996 .

[35]  Luke F. Lester,et al.  Frequency entrainment in optically injected semiconductor lasers , 1997 .

[36]  Jose Faro,et al.  An approximation for prey-predator models with time delay , 1997 .

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

[38]  Seon Hee Park,et al.  MULTISTABILITY IN COUPLED OSCILLATOR SYSTEMS WITH TIME DELAY , 1997 .

[39]  Deliang Wang,et al.  Relaxation oscillators with time delay coupling , 1998 .

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