The Application Of Disturbance Theory In Two-party Competition Based On The Law Of Mass Action

Competition is a universal law of nature and economic society.Resources are limited,but there is more than one that has demand for this resource,that leads to competition for this resource due to egoism and exclusivity,so that they can get this resource as much as possible and forms a competitive advantage.The competitive resource transfer method can refer to the law of mass action,so that the transfer coefficient is proportional to the amount of resources of each party,and the multi-party competition model established has reference significance.In this paper,a competitive model based on the law of mass action is proposed,and then the approximate analytical solution of the model is solved by using the disturbance theory,finally we analyze the effectiveness of the model and the final result of competition.The main research content of this paper is:The first chapter mainly expounds the background and literature review of competition research,then introduces the law of mass action and perturbation theory,and finally briefly describes the framework of this thesis.We proposes a simple competition model under the situation of competition between the two parties in the second chapter.We assume that the competitive attractiveness of the competing parties is only one small parameter difference,and the corresponding approximate solution is obtained through perturbation theory,and then the result is confirmed by comparison with the numerical solution,and finally the final result is discussed.The results show that different initial values will lead to different competitive results,and there is also a threshold of competitive attractiveness gap,beyond which the situation of two parties competing for resources will reverse.Building on the second chapter,the third chapter introduces the mutual transformation factor to make it more realistic.Similarly,the perturbation theory is used to obtain an approximate solution for small parameters,and the comparison with the numerical solution also proves the validity of the results.Then,the track analysis method is used to find that the model has two equilibrium points.The final resource allocation is the same as the non-zero equilibrium point,only related to the mutual conversion coefficient,and has nothing to do with the competitive attractiveness and initial value.Chapter 4 summarizes the article and points out the shortcomings of the model and where it can continue to be improved.