Diffusive coupling, dissipation, and synchronization

We consider the synchronization of diffusive coupled systems in situations where the synchronization is a consequence of the dissipation in the coupling as well as ones where there is an interaction between the inherent damping in the subsystems and the coupling. It is not required that the subsystems be identical, and they are allowed to have chaotic dynamics. Both discrete and continuous versions are discussed. We also consider coupled oscillators where the dynamics of each oscillator is determined by circuitry across a lossless transmission line.

[1]  J. Nagumo,et al.  Self-Oscillation in a Transmission Line with a Tunnel Diode , 1961, Proceedings of the IRE.

[2]  R. Brayton.  Bifurcation of periodic solutions in a nonlinear difference-differential equations of neutral type , 1966 .

[3]  D. W. Krumme,et al.  Differential-difference equations and nonlinear initial-boundary value problems for linear hyperbolic partial differential equations , 1968 .

[4]  D. Hoff,et al.  LARGE TIME BEHAVIOR OF SOLUTIONS OF SYSTEMS OF NONLINEAR REACTION-DIFFUSION EQUATIONS* , 1978 .

[5]  W. Fitzgibbon.  Strongly damped quasilinear evolution equations , 1981 .

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

[7]  P. Massatt.  Limiting behavior for strongly damped nonlinear wave equations , 1983 .

[8]  Jack K. Hale,et al.  Large Diffusivity and Asymptotic Behavior in Parabolic Systems. , 1986 .

[9]  M. A. Miller.  Nonuniqueness of inverse problems in macroelectrodynamics. Spherical and toroidal sources of electromagnetic fields (review) , 1986 .

[10]  M. Rabinovich,et al.  Stochastic synchronization of oscillation in dissipative systems , 1986 .

[11]  On the explicit construction of an ODE which has the same dynamics as a scalar parabolic PDE , 1987 .

[12]  S. Strogatz,et al.  Synchronization of pulse-coupled biological oscillators , 1990 .

[13]  A. Lichtenberg,et al.  NONLINEAR DYNAMICS OF SELF-SYNCHRONIZING SYSTEMS , 1991 .

[14]  Louis M. Pecora,et al.  Synchronizing chaotic circuits , 1991 .

[15]  Phase-locking effects in a system of nonlinear oscillators. , 1991, Chaos.

[16]  A. Lichtenberg,et al.  NUMERICAL AND EXPERIMENTAL STUDIES OF SELF-SYNCHRONIZATION AND SYNCHRONIZED CHAOS , 1992 .

[17]  Roy,et al.  Tracking unstable steady states: Extending the stability regime of a multimode laser system. , 1992, Physical review letters.

[18]  Dmitry E. Postnov,et al.  SYNCHRONIZATION OF CHAOS , 1992 .

[19]  T. Carroll,et al.  Synchronizing nonautonomous chaotic circuits , 1993 .

[20]  Leon O. Chua,et al.  On Chaotic Synchronization in a Linear Array of Chua's Circuits , 1993, J. Circuits Syst. Comput..

[21]  BIFURCATION SCENARIO OF A THREE-DIMENSIONAL VAN DER POL OSCILLATOR , 1993 .

[22]  Roy,et al.  Coherence and phase dynamics of spatially coupled solid-state lasers. , 1993, Physical review. A, Atomic, molecular, and optical physics.

[23]  Leon O. Chua,et al.  TRANSITIONS IN DYNAMICAL REGIMES BY DRIVING: A UNIFIED METHOD OF CONTROL AND SYNCHRONIZATION OF CHAOS , 1993 .

[24]  Nikolai F. Rulkov,et al.  Threshold synchronization of chaotic relaxation oscillations , 1993 .

[25]  Leon O. Chua,et al.  CONTROLLING CHAOS WITHOUT FEEDBACK AND CONTROL SIGNALS , 1993 .

[26]  Jack K. Hale,et al.  Introduction to Functional Differential Equations , 1993, Applied Mathematical Sciences.

[27]  Nikolai F. Rul'kov,et al.  Synchronized chaos in electronic circuits , 1993, Optics & Photonics.

[28]  Leon O. Chua,et al.  Chaos Synchronization in Chua's Circuit , 1993, J. Circuits Syst. Comput..

[29]  A Scalar Parabolic Equation Whose Asymptotic Behavior Is Dictated by a System of Ordinary Differential Equations , 1994 .

[30]  Roy,et al.  Experimental synchronization of chaotic lasers. , 1994, Physical review letters.

[31]  Nikolai F. Rulkov,et al.  Synchronous chaotic behaviour of a response oscillator with chaotic driving , 1994 .

[32]  Carroll,et al.  Synchronous chaos in coupled oscillator systems. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[33]  J. Hale.  Coupled Oscillators on a Circle , 1994 .

[34]  Hildebrando M. Rodrigues,et al.  Uniform Ultimate Boundedness and Synchronization for Nonautonomous Equations , 1994 .

[35]  Leon O. Chua,et al.  SPATIOTEMPORAL STRUCTURES IN DISCRETELY-COUPLED ARRAYS OF NONLINEAR CIRCUITS: A REVIEW , 1995 .

[36]  C. Tresser,et al.  Master-slave synchronization from the point of view of global dynamics. , 1995, Chaos.

[37]  Michael Peter Kennedy,et al.  SYNCHRONIZATION THEOREM FOR A CHAOTIC SYSTEM , 1995 .

[38]  S. Strogatz,et al.  Stability of Synchronization in Networks of Digital Phase-Locked Loops , 1995 .

[39]  Gang Hu,et al.  FEEDBACK CONTROL OF CHAOS IN SPATIOTEMPORAL SYSTEMS , 1995 .

[40]  Brian D. Sleeman,et al.  WAVE FRONT PROPAGATION AND ITS FAILURE IN COUPLED SYSTEMS OF DISCRETE BISTABLE CELLS MODELLED BY FITZHUGH-NAGUMO DYNAMICS , 1995 .

[41]  Shui-Nee Chow,et al.  Synchronization in lattices of coupled oscillators , 1997 .

[42]  Hildebrando M. Rodrigues,et al.  Upper Semicontinuity of Attractors and Synchronization , 1998 .