Abstract
The nonlinear dynamics of a chain of four coupled anharmonic oscillators with alternating frequency parameters is investigated. This system is treated as an elementary fragment of a discrete modulated nonlinear medium, in particular, a medium of magnetic and elastic nanoclusters and coupled optical waveguides. The stationary monochromatic oscillations of the system are investigated analytically and numerically, and a complete classification of them is carried out. The bifurcation diagram for such a system is obtained: the spectral dependences of the oscillation frequencies on the integral of the number of states are found. A detailed investigation of the bifurcation process for the appearance of an excitation which is an analog of the gap soliton in a finite-size modulated medium is carried out.
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