The Research Of Delay Differential Equation In The Application Of Several Economic Models

Among several areas, including Engineering Mechanics, EcologicalEnvironment and Financial Economics, delay differential equation, with thecharacteristic of time lag, have a wide range of applications. In this paper weconsider several classical mathematical models in the economics, and improve them.Considering the actual economic situation, delay parameter is introduced in thispaper for the first time. We study the stability of equilibrium point in systems, theexistence of periodicity and Hopf bifurcation. All of these provide new methods andthoughts to solve the related problems.The main creativities in the paper are as follows:Firstly, we analyze the national comprehensive strength model, building thedelay model of enterprise comprehensive strength. On the basis of the distributionof the linear root which closes to the system balance, we find out the stability of thesystem balance and the conditions of existence for Hopf bifurcation and make thephase diagram analysis of the system and get the economic significance.Secondly, it introduces the competition model and cooperation model amongthe biotic populations, building the cooperative and competitive mathematicalmodel between the cluster enterprises. Then it gets the condition which can makethe system stable by doing the research about equilibrium point stability and Hopfbifurcation existence with the main monomial analysis. Lastly, it makes the phasediagram analysis of the system and gets the economic significance.Finally, it introduces time delay feedback control model of the energyconsumption system, and builds the time delay model of Shandong energy supplyand demand on the basis of that. Then it gets the condition which can make thesystem stable by doing the research about equilibrium point stability and Hopfbifurcation existence with the main monomial analysis. Next, it achieves the resultusing the Matlab software to make numerical simulation, and proves the reliabilityof the theoretical proof. Lastly, it makes the phase diagram analysis of the systemand gets the economic significance.