Research On Key Techniques Of Radio Resource Allocation In Relay-enhanced Cellular Networks

The spread of rumor has a great influence on people’s lives and social stability. With the advent of the information age coming, the rumor spread in the network more quickly and widely. Its destructive power has surpassed any previous era. In order to maintain the harmony and stability of society, we must thoroughly study the mechanism and development trend of rumor spreading, then we can take further effective measures to control the spread of rumor in the network. Therefore, the main research method of rumor spreading is establishing dynamic model of rumor spreading, analysising dynamic characteristics based on the model, and controling some dynamic phenomenon. On the base of SIR model, this paper proposes an improved rumor spreading model, then this paper analyzes the dynamic characteristics of the new model and puts forward some appropriate methods for dynamic control. The main work of this paper is as follows:1,This paper proposes a new rumor spreading model and analyzes the dynamic behavior of the new model. This paper finds out several stable nodes of the new model and analyzes the existing conditions of the stable nodes. Then it analyzes the local stability and global stability of the system near the stable nodes. And the analysis is verified by MATLAB simulation.2,This paper analyzes the Hopf bifurcation phenomenon near the stable nodes and studies the asymptotic stability and instability phenomenon in the model. This paper analyzes the direction and criticality of Hopf bifurcation, the paper studies the expression of the limit cycle amplitude and studies the control method of the limit cycle amplitude, which can effectively increase or decrease the amplitude of the limit cycle. And the analysis is verified by MATLAB simulation.3,By using the method and theory of optimal control, the existence of optimal solution is proved.And then this paper derives the optimal control function. This paper compares the evolution process of the model before and after adding control function.The simulation result shows the effectiveness of the optimal control, which can make the number of people who spread rumor over a period of time at least.