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A mathematical description is presented and an analysis is realized of the behavior exhibited by electrochemical systems in which the anodic dissolution (cathodic deposition) in a potentiostatic regime is accompanied by the formation of a passivating film at the electrode surface. It is demonstrated that certain regions of the system’s parameters are characterized by the instability of steady states and by spontaneous transition to the multiplicity of steady states or to an oscillatory regime. The reason for the emergence of oscillations is the presence of the stage of the formation and dissolution of the passivating film on the electrode surface. Mathematical description of the stages of the formation and dissolution of the passivating film substantially depends on the film’s thickness. Considered is a thin film, which comprises a few monolayers and which is represented as a two-dimensional phase, with the alteration of an activation energy as a function of the coverage θ taken into account. It is demonstrated, by considering a mechanism of the anodic metal oxidation in an acid environment, that accounting for the specific features of the passivation stage successfully explains the emergence of the oscillations and the multiplicity of steady states and the necessary and sufficient conditions for their realization are found. Bifurcation diagrams are constructed in the plane of kinetic parameters of the system. The conditions leading to the emergence of a hysteresis loop are shown. The vertical inflection in an i, V curve at the point of an active-passive transition is explained.

Finite-difference techniques in the frequency domain (FDFD) method was used for calculation of the integrated-optical structure. As an example of the structure the signal distribution between optical waveguides linked by the ring resonator was investigated. The amplitude-frequency dependence for the structure was calculated with a spectral method. The used method allows to calculate not only exact position of spectral components, which correspond to the same one calculated analytically, but can also predict the relation between amplitudes of spectral components.