The Stability Of Two Kinds Of Economical Models With Time Delay And The Research Of Hopf Branch Direction

Differential equations with delay are differential equations with time delay or lag,because they take into account the influence of history on the current state,so they have been widely used in biology,mechanics,economics and other fields.The first chapter summarizes the historical background and significance of the problem research,and briefly introduces the research status of the problem and some related preliminary knowledge.The second chapter takes a kind of comprehensive national power model with time delay as the research object,and studies the stability of comprehensive national power development under the action of time delay feedback.Firstly,using the branch theory and stability to obtain the positive balance characteristics of the system;then take the time lag As a branch parameter,when the branch point is passed,the stability of the system's positive equilibrium is changed.This not only eliminates the chaotic phenomenon,but also branches off the periodic orbit.Using the method and the central manifold theorem,the direction and stability of the periodic solution are obtained.The sex determination formula.Finally,the numerical simulation of the dynamic behavior of a time-delay controlled system with parameters is performed to verify the validity of the analytical results.The third chapter studies a kind of three-dimensional financial enterprise competition model with two time delays.Using time-delay and branch parameters,branch theory is used to determine whether there is a periodic orbit in a financial system with time-delay,and the characteristics of the positive balance point of the system.Discussed,using the normal method and the central manifold theorem to further determine the direction and stability of the periodic solution formula.Finally,the theoretical analysis results have been verified through numerical simulation,providing a better understanding and development of the market for business managers Theoretical basis.The fourth chapter mainly summarizes and reviews the full text,and also forecasts the issues to be studied.