Journal of Advances in Applied Mathematics

7

Authors: Linlin Shen, Jingbo Zhou, Longcheng Xing, Xiaodong Pan, Yu Zhang

This paper mainly studies the cooperative evolution of game model on the regular lattice, and to explore factors that influence the evolution of cooperation, including proportion of initial betrayers, the game model, the profit ratio, the number of neighbors that profit information, and the policy update rules. The results show that: Different factors have different effects on the evolution of cooperation. The proportion of initial traitors has no effect on the evolution of cooperation (except in extreme cases). The profit ratio has a great influence on the evolution of cooperation. The different profit ratio has a direct impact on the stability of cooperation evolution, and the stable state of the profit ratio between 1.8 and 2.0 is almost the same. Policy update rules are the most important factors affecting the evolution of cooperation, and different rules determine the ratio of cooperation when the evolution of cooperation is stable. With the increase in the number of neighbors that profit information, the ratio of cooperation is steadily rising when cooperation is stable. Prisoner's dilemma is more cooperative than snowdrift game.

11

Authors: Zhen Li

We describe the periodic dilution rate and periodic mortality of a stochastic chemostat model with the response of the Monond function. We consider that both nutrient’s input concentration and the death rate of microbe are simultaneously influenced by white noise. For this chemostat, we have found sufficient conditions which have a stationary distribution and stochastic nontrivial positive periodic solution.

12

Authors: Longcheng Xing, Linlin Shen, Xiaodong Pan, Jingbo Zhou, Fuqiang Sun

In this paper, the flow field and aerodynamic noise of a simple automotive rearview mirror are analyzed by using Star CCM + software. The external flow field and aerodynamic noise of the rearview mirror are studied by adding a guide bar to the mirror model. The variation of the external flow field and the noise of the rearview mirror are studied by changing the height of the guide bar(3mm,6mm,10mm).The results show that the pressure difference between the windward side and the leeward side of the rearview mirror is an important factor causing the airflow resistance. The location of the surface sound source of the rearview mirror is mainly concentrated in the A-pillar area. The rear-view mirrors with 10mm guide bar weaken the pressure gradient generated by the airflow through the rearview mirror, and the airflow separation and re-attachment are small, which significantly deviates from the support facing the vortex position of the vehicle outflow field, reducing the effect of turbulent pulsating pressure on the support surface, and the pressure pulsation is superior to the other two cases.