| Parametrized Kuramoto Model for Coupled Oscillators with Fractional Frequencies Ratios |
|
 |
|
|
| Authors |
| | Gourary M.M. |
| | Rusakov S.G. |
| Date of publication |
| | 2020 |
| DOI |
| | 10.31114/2078-7707-2020-1-40-45 |
|
| Abstract |
| | The paper proposes modifications of the Kuramoto model providing its application to the problems of the circuit simulation. The development of the parametrized Kuramoto model was based on the smoothed form of the PPV macromodel earlier proposed by authors.
Proposed parametrized model of a Kuramoto oscillator is based on harmonics of the oscillator waveform and the oscillator PPV harmonics representing the oscillator sensitivity to the excitation. All harmonics for the model parametrizing can be obtained by the simulation of the free-running oscillator.
Dynamic couplings are parametrized by frequency-depended transfer functions of linear interconnects included in the model. The frequency argument of the transfer function is defined by the time derivative of the corresponding phase variable. Such an approach saves the order of the model’s ODE system.
For the first time, the problem of analyzing a system of coupled oscillators with close to a fractional ratio of natural frequencies is considered. Previously, the Kuramoto model was used to analyze oscillatory systems with close frequencies only. An approach to the model construction is based on the transformation of the oscillatory equation to the equation with a multiple period. The developed model contains numerators and denominators of rational fractioons as additional parameters affecting the presentation of the phase argument of coupling functions. |
| Keywords |
| | coupled oscillators, Kuramoto model, phase macromodel, synchronization, dynamical system. |
| Library reference |
| | Gourary M.M., Rusakov S.G. Parametrized Kuramoto Model for Coupled Oscillators with Fractional Frequencies Ratios // Problems of Perspective Micro- and Nanoelectronic Systems Development - 2020. Issue 1. P. 40-45. doi:10.31114/2078-7707-2020-1-40-45 |
| URL of paper |
| | http://www.mes-conference.ru/data/year2020/pdf/D002.pdf |
