Synchronization in a ring of four mutually coupled van der Pol oscillators: theory and experiment.

We investigate different states of synchronization in a ring of four mutually coupled van der Pol oscillators. The stability analysis and numerical simulation are performed to determine the suitable coupling parameters leading to high-quality synchronization. The consequences of parameter mismatch are also highlighted. Experimental realization is then used to show the existence of complete and partial synchronization.

[1]  Effects of the deviation of element values in a ring of three and four coupled Van der Pol oscillators , 1999 .

[2]  M. Golubitsky,et al.  Symmetry in locomotor central pattern generators and animal gaits , 1999, Nature.

[3]  Ian Stewart,et al.  A modular network for legged locomotion , 1998 .

[4]  I. Stewart,et al.  Coupled nonlinear oscillators and the symmetries of animal gaits , 1993 .

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

[6]  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.

[7]  Martin Golubitsky,et al.  Heteroclinic cycles in rings of coupled cells , 2000 .

[8]  Hilda A. Cerdeira,et al.  Coupled chaotic oscillators and their relation to a central pattern generator for artificial quadrupeds , 2005 .

[9]  D. Huber Corrections to the Mori-Kawasaki approximation for the high temperature limit of the spin diffusion constant for a magnetic lattice☆ , 1970 .

[10]  Ned J. Corron,et al.  A new approach to communications using chaotic signals , 1997 .

[11]  S. Boccaletti,et al.  Synchronization of chaotic systems , 2001 .

[12]  Ying Zhang,et al.  Experimental investigation of partial synchronization in coupled chaotic oscillators. , 2003, Chaos.

[13]  M. Golubitsky,et al.  Models of central pattern generators for quadruped locomotion I. Primary gaits , 2001, Journal of mathematical biology.

[14]  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.

[15]  Ricardo Femat,et al.  Synchronization of a class of strictly different chaotic oscillators , 1997 .

[16]  H. Cerdeira,et al.  Partial synchronization and spontaneous spatial ordering in coupled chaotic systems. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.