基于频率权重耦合模型的多层复杂网络爆发式同步

Explosive synchronisation of multi-layer networks based on frequency-weighted coupled model

同步现象是复杂网络和系统中普遍存在的一种动力学行为.针对多层复杂网络上产生爆发式同步的临界耦合强度问题,提出一种多层频率权重耦合的Kuramoto模型,通过平均场思想和自洽理论分析求出多层复杂网络上产生爆发式同步时的临界耦合强度值,并进行了仿真验证.理论分析和仿真结果表明,该临界值与层间相互作用强度和网络平均度相关,层与层之间的相互作用增强会阻碍爆发式同步的产生,而网络平均度增大会促进爆发式同步的产生.这一结果对复杂网络和复杂系统的研究具有重要意义.

Synchronisation is a prevalent and universal dynamic behaviour of complex systems.Based on the critical coupling strength of explosive synchronisation in multi-layer complex networks,a frequency-weighted Kuramoto model was developed in this study.We obtained the critical coupling strength for explosive synchronisation through field tests,self-consistent analysis,and numerical simulation.The theoretical analysis and simulation results show that the critical value is related to the strength of the interlayer interaction and the average degree of the network.Increasing the interaction between layers prevents explosive synchronisation,whereas increasing the average degree of the network facilitates explosive synchronisation.The results are useful for studies on complex networks and systems.