Dispersion relations of the lattice of global coupling oscillators

 

V. N. Kornienko ¹⁾, A. P. Privezentsev ²⁾, V. A. Cherepenin ¹⁾

¹⁾ Kotel’nikov Institute of Radio-engineering and Electronics, Fryazino branch

²⁾ Chelyabinsk State University

 

Received June 12, 2013

 

Abstract. We obtain the dispersion relations for the two-dimensional lattice and the one-dimensional chain of oscillators coupled by a common field. The two cases (when the communication is done through the displacement of oscillators and their time derivatives) were considered. The closed dispersion equations, which containing elementary functions only, were obtained in one-dimensional case. The analysis of the behavior of dispersion characteristics for the various parameters of the system was done.

Keywords: metamaterials, oscillators, global coupling.