The European Physical Journal Applied Physics

Physics of Energy Conversion and Coupled Phenomena

Simultaneous and sequential synchronisation in arrays

G. Ambikaa1 and K. Ambikaa2

Indian Institute of Science Education and Research, Pune, India

Department of Physics, Maharaja's College, 682 011 Ernakulam, Kerala, India


We discuss the possibility of simultaneous and sequential synchronisation in vertical and horizontal arrays of unidirectionally coupled discrete systems. This is realized for the specific case of two dimensional Gumowski-Mira maps. The synchronised state can be periodic, thereby bringing in control of chaos, or chaotic for carefully chosen parameters of the participating units. The synchronised chaotic state is further characterised using variation of the time of synchronisation with coupling coefficient, size of the array, etc. In the case of the horizontal array, the total time of synchronisation can be controlled by increasing the coupling coefficient step wise in small bunch of units.

(Received July 10 2006)

(Accepted December 11 2006)

(Online publication January 24 2007)


  • 05.45.Xt – Synchronization; coupled oscillators;
  • 05.45.-a – Nonlinear dynamics and chaos