stability.

The review of works on studying artificial media with negative refractive index and  their unique application is given. We make a point of negative refraction and lens effects in plan-parallel  layers of such metamaterials. The properties and stability conditions of waveguide modes in  layered structures and open cavities are considered in terms of the effective diffraction and  dispersion lengths.

The paper considers a self­organized critical process of clasterization. The stability of the equilibrium for infinite system of the differential equations approximating this process is proved.