| Due to the rapid social progress and development of society,most college students choose to study abroad in order to pursue better development space.At the same time,in order to cultivate more social talents,there are more and more international cooperation programs among colleges and universities.English level has become an important indicator for college students to study abroad.Through many previous studies,it was found that there is a certain relationship between English proficiency and students’achievement in various subjects.This is mainly due to the fact that the teaching materials of students participating in Sino-US cooperation schools are all English textbooks,and students are taught in English.However,Empirical studies that examine gender difference in English proficiency of undergraduate students from the cooperative education programs are rare.Due to the influence of Chinese traditional campus culture,college students from the same class will be concentrated in dormitories on the same floor.This means that students with poor learning habits are likely to have a negative impact on roommates and close classmates with lower self-control.On the one hand,this paper mainly studies the gender and urban-rural differences of English learning and the influence of English learning on the performance of professional courses,on the other hand,it studies the dynamic state analysis of the negative effects of poor students on other students.The details are as follows:First of all,it introduces the background of Sino-US cooperative education,the specific research contents,the relevant theoretical knowledge of ordinary differential equations and the specific principles of research methods.Secondly,the collected data be used to do correlation analysis between variables by use IBM SPSS software and use IBM SPSS AMOS（23）software to do path analysis,analyze the relationship about the scores of English entrance,gender,locality,English scores and academic performance of the first year,English scores and academic performance of the second year.From the conclusion of the analysis,it can be seen that the English level of the students is not improved steadily,and the students from different locality are only slightly difference in the English entrance.However,from the results of the college students’English study,there is a significant difference between the students’English performance and their gender,then the results of the mathematics curriculum（represented by the GPA of all the courses）are also affected by the English results.Thirdly,to study negative social influences of poor students on other students’learning motivation,and establishes a mathematical model by constructing a series of nonlinear ordinary differential equations.The system is divided into ideal state（all students passing）,the sub-ideal state（no student need resitting any course）and the real state（some students pass all their examinations,others have to make-up examinations,resit courses or even dropout）.Use threshold parametersR01 andR02,separately explain the existence and stability of these three states,and threshold parametersR01 andR02 have similar significance to the basic reproduction number of mathematical epidemiology.When the drop-out rates are less affected by negative society,the model is shown to have a backward bifurcation atR02（28）1.This result is also illustrated by numerical evidence.To establish guidelines for effective policies to prevent students from falling grades or even being dropped out of school,sensitivity analyses are performed for bothR01 andR02,and the specific educational measures are put forward from the point of view of mathematical analysis.Finally,the influence between bad students and good students is a long-term process,because in the short term,the negative effect between students is not immediately apparent through the academic performance of students and the mechanism of the negative effect of bad students on the normal students（who pass all the examinations）is not very clear.In addition,it is assumed that the campus atmosphere plays a random role on the academic performance of students.It is for the above reasons that,on the basis of the above-mentioned model,we establish the stochastic differential equation with delay effects and further quantitatively study this effect.Finally,we summarize the paper according to the research contents. |
