Анализа и управување на осцилаторно придушување на спрегнати осцилаторни системи преку временско-променливи функции на спрега

Abstract

In this doctoral thesis we analyzed the effect of time-varying coupling functions on the oscillation quenching mechanisms. We showed that the time-varying coupling functions introduce a degenerative dimension in the interaction between oscillators that leads to cessation of the oscillations. A special case of coupling function variability was considered, the form of the coupling function changes in time, while the net-coupling strength is constant. Under the assumed variability, the considered time-varying coupling function took the discussed systems through a series of qualitative transitions between oscillatory and quenched states. During our investigation of the time-varying interactions, we discovered that the coupling functions can be responsible for the manifestation of uncountable, stable and unstable, non-trivial steady states, that have their own, characteristic structure and basin of attraction. The emergence of this regime, not observed in literature until now, can trigger a transition from oscillatory to non-oscillatory state or transitions among different oscillatory and non-oscillatory states, under perturbation or noise. The cessation of the oscillatory process should be avoided at all costs in numerous systems with intrinsic oscillatory dynamic. Having this in mind, we designed a control approach that detects and prevents the emergence of an oscillation quench state. The effectiveness of the proposed control algorithm was tested on a coupled system that normally, without control, undergoes a transition from oscillatory to oscillation quench state. After we incorporated the designed control approach the oscillations persisted in the coupled system over the observed period of time.