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Role of Non-Reciprocity in the Theory of Oscillations
Radio Physics and Radio Astronomy, Vol. 23, #1, pp.60-71 (2018)

V.A. Buts and D.M. Vavriv

Purpose: The dynamics of coupled linear oscillators is investigated under the nonreciprocal coupling between them in order to determine the possibility of transferring the energy of low-frequency oscillations to the energy of high-frequency oscillations. Design/methodology/approach: The methods of the theory of dynamical systems were used. In particular, the singular perturbation theory, the theory of secondary resonances, and the averaging method. Methods of numerical analysis were also used. First, the analysis of dynamics of a system of two identical linear high-frequency oscillators was made . These oscillators are connected by a weak non-reciprocal coupling. It was shown that in the presence of a non-reciprocal coupling, the complex amplitudes of high- requency oscillators can be parametrically enhanced. If the connections were mutual, there was no such increase. Further, the dynamics of a large number of high-frequency linear oscillators was studied. It was shown that when the oscillators were linked by mutual coupling , their initial energy was practically unchanged. Under the nonreciprocity, the possibility of parametric amplification of the amplitudes of high-frequency oscillations occurred. The dynamics of two coupled nonlinear oscillators was also considered. The singular perturbation theory was used and it was shown that if the coupling coefficients are mutual, then there is an integral, which does not allow to transform the energy of low- requency external perturbations into the energy of high-frequency oscillators. The presence of non-reciprocal bonds destroys this integral, and the energy conversion channel opens. The analysis of the numerical results fully confirmed the analytical results obtained. In conclusion, the possibilities of using the detected channel are analyzed. Potentially, it can be used in any frequency interval. Actually, at present, it is useful in millimeter, submillimeter and terahertz ranges. Findings: It is shown that the presence of a nonreciprocal coupling between high-frequency oscillatory degrees of freedom opens up a channel for transferring energy from low-frequency oscillations to energy of high- requency oscillations. Key words: oscillators, non-reciprocal coupling, oscillation generation, dynamical systems