Research On The Synchronization Dynamics Of The Amplitude Envelope In The Coupled Oscillators System

Many self-organizing dynamic behaviors of coupled vibration subsystem are closely related to the functional realization of the system,among which various forms of synchronization is the most common one.The interaction of coupled oscillator units with different frequencies will form amplitude envelope,and the amplitude envelope also shows various correlations under the coupling effect,such as different forms of amplitude envelope synchronization(complete synchronization,phase synchronization,reverse synchronization,and extended state).The amplitude envelope dynamics of coupled systems are closely related to many system functions,such as signal transmission control in the field of communication,neuron potential change in the field of biomedicine,disease control,etc.Much attention has been paid to the generation mechanism,main characteristics and general rules of dynamic behavior of coupled vibration subsystem amplitude envelope.Through theoretical modeling and numerical simulation,the dynamic stability of amplitude envelope synchronization is studied deeply.1.Complete synchronous dynamics of amplitude envelope of coupled vibration subsystem.Based on a simple coupled periodic oscillator model,the stability conditions and the main intrinsic characteristics of the complete synchronization of the amplitude envelope between the coupled oscillators are analyzed.2.Extended state of amplitude envelope in global coupled vibration subsystem.By introducing a heterogeneous oscillator in a globally repulsive coupled homophonic network,extended states based on amplitude envelope can be observed in other homophonic subsystems.By transforming the polar coordinates of the vibration subsystem model,the evolution equation of the amplitude envelope is derived under the weak coupling approximation condition,and the theoretical values of the main characteristic quantities of the amplitude envelope(mean value,amplitude and period)in the extended state are determined.By comparison,the theoretical and numerical results agree well with each other in the case of weak coupling and large frequency mismatch.In addition,the amplitude envelope extension state is also observed in coupled Fender wave subsystems,which shows that this phenomenon is universal.3.Reverse phase synchronization of amplitude envelope in coupled vibration subsystem.In the attraction-coupled subsystem,the repulsive coupling is introduced,and the amplitude envelope of the coupled subsystem will change from complete synchronization to reverse synchronization under the competition between them.Through theoretical analysis,the approximate analytical solution of the amplitude envelope of the coupled oscillator in reverse phase synchronization is derived,and the results are in good agreement with the numerical calculation.4.Transition analysis of amplitude envelope from reversed-phase synchronization to complete synchronization in coupled Josephson junction circuit.The transition process of the amplitude envelope of coupled Josephson junction circuit system from reverse phase synchronization to complete synchronization under different coupling strength and damping coefficient is discussed.The results show that under weak coupling and low damping,the amplitude envelope is approximately antiphase synchronous,and under strong coupling and high damping,the amplitude envelope is approximately completely synchronous.In this paper,the in-depth exploration of the synchronous dynamic behavior of the amplitude envelope of coupled oscillators and the theoretical analysis of the amplitude envelope proposed in this paper are conducive to the understanding of the essence of the synchronous behavior of the amplitude envelope.It provides possible theoretical guidance for the analysis of EEG and neuronal potential changes and semantic recognition in biomedical field.