Research On Oscillation Recovery Problem Based On Weight Feedback

The maintenance of stable and rhythmic activities is a prerequisite for the normal operation and evolution of many systems.However,the oscillation quenching phenomenon will destroy the oscillation activities of the system itself and hinder the normal operation of the system.Therefore,the inverse problem of oscillation quenching,namely oscillation recovery,has attracted the attention of many scholars.In order to recover the system oscillation that disappeared due to oscillation quenching,this paper improve the feedback strategy proposed by predecessors,constructed a new feedback item,and apply it as an external feedback to each vibration subsystem model,and finally prove that it could recover all kinds of system oscillation.The main work of this paper is summarized as follows:Average field feedback is a special case of weighted feedback.In order to discuss whether the average field feedback is the optimal weighted feedback,we extend the average field feedback to a more general form,namely weighted average feedback,and try to find the optimal weight.Theoretical analysis and numerical simulations demonstrate that the best recovery of system oscillations is achieved when the weight is 0 or 1,that is,when there is a single oscillator in the system as a feedback,and only the state information of one oscillator needs to be known at this time.In contrast,the previous feedback strategy needs to know the state information of all oscillators in the system.Therefore,this strategy greatly reduces the difficulty of obtaining required information and effectively improves the practical application of the strategy.The oscillation quenching can be regarded as the system achieving a balance in a certain sense with the final steady-state as the axis of symmetry,while the asymmetry factor can help us destroy the system symmetry.Therefore,we combine the asymmetry factor and the average field feedback and extend it to a more general form,namely the weighted asymmetric feedback,and apply different feedback intensities to different oscillators.Theoretical analysis and numerical simulations demonstrate when the weight is 0 or 1,that is,the feedback only acts on a single oscillator in the system,the system oscillation recovery effect is the best.At this time,feedback only needs to be added to the oscillator that is easiest to feedback in the system,and the system oscillation can be effectively restored.Compared with the previous feedback strategy,feedback needs to be added to all oscillators at the same time.Therefore,this strategy greatly reduces the difficulty of adding feedback to the system and effectively improves the practical application of the strategy.Weighted average feedback and weighted asymmetric feedback are complementary in a sense,so we combine weighted average feedback and weighted asymmetric feedback to get double weighted feedback.Through theoretical analysis and numerical simulation,it is finally proved that when the two weights are 0 or 1,that is,when a single oscillator acts as feedback and only acts on the oscillator,the oscillation quenching can be effectively eliminated.This method has the advantages of the first two methods and can recover the system oscillation more simply and effectively.