Research On Fast Collective Synchronization Of Kuramoto-Oscillator Networks

In recent years,the fast cluster synchronization problem of Kuramoto-oscillator networks,as a hot research topic of complex dynamic network,has developed rapidly,and the research results are endless.Among these results,there are a lot of research and study on finite-time and fixed-time synchronization of Kuramoto-oscillator networks.However,in the current research on the finite-time and fixed-time synchronization of Kuramoto-oscillator networks,the effect of environmental noise on the synchronization of the oscillator-networks is not considered.In addition,chattering phenomenon is common in the process of achieving finite-time and fixedtime synchronization of Kuramoto-oscillator networks,which greatly affects the synchronization performance of the network.Under this background,this paper further explores the finite-time and fixed-time synchronization of stochastic Kuramoto-oscillator networks with environmental noise disturbance by designing a new smooth control protocol.The main research contents include:(1)By designing a new and smooth fixed-time control protocol and a switching control protocol,the sufficient conditions for achieving the fixed-time phase agreement and frequency synchronization of the Kuramoto-oscillator networks are obtained by using the stability analysis theory.The upper bound of convergence time independent of the initial state of the oscillators is given,which eliminates the chattering phenomenon caused by the signum function in the synchronization process and reduces the control cost of the fixed-time synchronization of the Kuramoto-oscillator networks.The validity and feasibility of the theoretical results are verified by numerical simulation.(2)Considering the effect of environmental noise on the synchronization of Kuramotooscillator networks,a smooth stochastic finite-time control protocol was designed to achieve finite-time phase agreement and frequency synchronization of the stochastic Kuramotooscillator networks.The sufficient conditions for achieving synchronization and the upper bound of convergence time were obtained,eliminating the chattering phenomenon caused by signum functions during the synchronization process.The validity and feasibility of the theoretical results were verified through numerical simulation.(3)Based on the research on the finite-time synchronization problem of stochastic Kuramoto-oscillator networks in this article,combined with the traditional fixed-time synchronization control protocol of Kuramoto-oscillator networks proposed in this article,further exploration was conducted on the fixed-time synchronization of stochastic Kuramotooscillator networks affected by environmental noise interference.By designing a reasonable random fixed-time control protocol,the fixed-time phase agreement and frequency synchronization of the stochastic Kuramoto-oscillator networks were achieved,and the synchronization process of the oscillator networks was also smooth.The numerical simulation results not only validate the correctness and effectiveness of the theoretical analysis,but also indicate that the Kuramoto-oscillator network’s process of achieving frequency synchronization is more sensitive to noise disturbances than the process of achieving phase agreement.In summary,based on the research on the synchronization problem of traditional Kuramoto-oscillator networks,combined with the designed smooth control protocol,innovative research is conducted on the finite-time and fixed-time synchronization problem of stochastic Kuramoto-oscillator networks.This achieved fixed-time synchronization of traditional Kuramoto-oscillator networks and the finite-time and fixed time synchronization of stochastic Kuramoto-oscillator networks,The synchronization time of the stochastic Kuramoto-oscillator networks is shortened and the synchronization performance of the Kuramoto-oscillator networks is improved.