Aging Transition With The Influence Of The Complex Networks' Structure

There are many network structures in nature.They have complex structural patterns,but their overall structure can be represented by network connections,and these structures can be classified by statistical principles.Among them,the scale-free network and the small-world network are two distinctive structures in complex networks,and they each obey their own distribution characteristics of some degree(the sum of out degree and in degree).This paper mainly studies the influence of degree on the aging of the entire system when the degree is used as a time-scale correlation factor in a complex network,and adds the feedback coefficient as a secondary research objective to explore the conditions under which these parameters promote or inhibit system aging The occurrence of the phenomenon.(1)Calculate the theoretical fixed point through the Jacobian matrix of the oscillator equation;(2)Use C++in Visual Studio to perform programming simulation experiments,and use the fourth-order Runge-Kutta method to simulate the motion trajectory of the oscillator,and obtain its simulation fixed point;(3)Comparison The simulation value and theoretical value of the oscillator equation verify the correctness of the theory.The first chapter of this article briefly describes the concept of amplitude death in complex networks and dynamics,and expounds the current research status in the field of aging.The second chapter describes a relatively common oscillator model in dynamic systems,and describes the formation process of the coupling equations in this article.The third chapter describes in detail the phenomenon that occurs in the case of scale-free network in the simulation experiment,and briefly analyzes the influence of the network structure parameters of the scale-free network on network aging.The fourth chapter is similar to the third chapter,describing the influence of the network structure parameters of the small world network on the network aging.The fifth chapter obtains the theoretical area of aging under the same conditions in the third chapter and the fourth chapter through theoretical derivation,and verifies the correctness of the theoretical value.Chapter 6 is a summary of the full text.It summarizes the influence of network structure parameters on network aging in Chapters 3 to 5,and analyzes the reasons for deviations from theoretical derivation in simulation experiments.