Stability of synchronization in a shift-invariant ring of mutually coupled oscillators

This paper treats synchronization dynamics in a shift-invariant ring of N mutually coupled self-sustained electrical units. Via some qualitative theory for the Lyapunov exponents, we derive the regimes of coupling parameters for which synchronized oscillation is stable or unstable in the ring.

[1]  David Hansel.  Synchronized Chaos in Local Cortical Circuits , 1996, Int. J. Neural Syst..

[2]  H. Jürgensen.  Synchronization , 2021, Inf. Comput..

[3]  Carroll,et al.  Short wavelength bifurcations and size instabilities in coupled oscillator systems. , 1995, Physical review letters.

[4]  Johnson,et al.  Three coupled oscillators as a universal probe of synchronization stability in coupled oscillator arrays , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[5]  Tianping Chen,et al.  New approach to synchronization analysis of linearly coupled ordinary differential systems , 2006 .

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

[7]  Frank Pasemann,et al.  Synchronized chaos and other coherent states for two coupled neurons , 1999 .

[8]  Li,et al.  Bifurcation to standing and traveling waves in large arrays of coupled lasers. , 1994, Physical review. A, Atomic, molecular, and optical physics.

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

[10]  On estimates of Lyapunov exponents of synchronized coupled systems. , 2006, Chaos.

[11]  Hansel,et al.  Synchronization and computation in a chaotic neural network. , 1992, Physical review letters.

[12]  P. McClintock.  Synchronization:a universal concept in nonlinear science , 2003 .

[13]  P. Holmes,et al.  Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.

[14]  M. Hasler,et al.  Connection Graph Stability Method for Synchronized Coupled Chaotic Systems , 2004 .

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

[16]  Chern.,et al.  Synchronization of mutually coupled self-mixing modulated lasers , 2000, Physical review letters.

[17]  Paul Woafo,et al.  Synchronization: stability and duration time. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  F. V. Atkinson,et al.  Discrete and Continuous Boundary Problems , 1964 .

[19]  Winful,et al.  Synchronized chaos and spatiotemporal chaos in arrays of coupled lasers. , 1990, Physical review letters.

[20]  T. Carroll,et al.  Master Stability Functions for Synchronized Coupled Systems , 1998 .

[21]  Tianping Chen,et al.  Synchronization of coupled connected neural networks with delays , 2004, IEEE Transactions on Circuits and Systems I: Regular Papers.

[22]  P Woafo,et al.  Synchronized states in a ring of mutually coupled self-sustained electrical oscillators. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.