Multidisciplinary Investigations On Some Complex Systems

This dissertation mainly investigates complex systems by combining different disciplines and thus provides new thoughts for studying various complex systems.The contents involve the investigation of nonlinear dynamical equations that describe interacting systems.This dissertation proposes characteristic function method to first obtain strict solutions of a class of nonlinear ordinary differential simultaneous equations,which are widely applied in the investigations of various complex systems(such as physical systems,ecological systems,economic systems,etc.),and thus people can further understand systems' dynamical behaviors.In Lagrange dynamics of the general economic system,by analogizing the economic systems with the multi-body scalar dynamics systems in physics and considering constraint conditions,this dissertation generalizes the Lagrangian of Pigou equilibrium model about public goods optimization distribution to the Lagrangian of the general economic system,and then gets Euler-Lagrange equations of the general economic system.Under certain conditions,the solutions of Pigou equilibrium model can be obtained from the discussions about Euler-Lagrange equations of the general economic system.Meanwhile,this dissertation gives the meaning of Lagrange multipliers in Euler-Lagrange equations,and gets dynamical quantities of the general economic system in the process of discussing Euler-Lagrange equations' solutions for the first time,which cannot be given in the usual theories.In addition,this dissertation investigates the theory of generation of financial crises from new,interesting and different from traditional macroeconomic analyses' viewpoint.Because the similarity between the propagation phenomenon of negative information about potential deterioration of economic situation in group of investors and the propagation phenomenon of infectious disease in crowd,based on the similarity and the idea of mathematical model of infectious disease,this dissertation builds the negative-information-propagation-induced model with dissipative construction,and utilizes the model to investigate the relationship between the generation of financial crises and propagation effects of negative information in group of investors.This dissertation introduces the discrimination parameter to distinguish whether or not the propagation of negative information will go through an ascending process in group of investors,and introduces the target critical value of financial crises.By comparing the ratio of the total number of investors after long enough time to the total number of investors at some time as initial time with the target critical value of financial crises,people can monitor whether the curve of total number of investors is progressing toward the direction of generating financial crises or running on track of financial markets safety in real time.If at some time this ratio is computed to be less than the target critical value of financial crises,governments should take relevant measures to prevent the generation of financial crises in advance.Governments' interference helps to recover the confidence of investors so that they never will again believe in negative information to continue their investment.Results from theoretical and numerical analysis show that the number of negative information holders,and the number of investors withdrawing capital and departing from financial markets when governments make appropriate interference are lowered.So this dissertation shows the effectiveness of governments in preventing financial crises from the viewpoint of the negative-information-propagation-induced model,namely governments' prevention against financial crises can reduce the possibility of the generation of financial crises.Besides discussing financial crises,this dissertation still investigates the relationship between currency and financial markets' economic situation by combining the mathematical model of infectious disease.This dissertation first gets the critical value of negotiable amount of currencies in storage.People can measure the size of potential financial risks in financial markets through comparing the critical value with initial negotiable amount of currencies in storage.This dissertation also first finds the critical value of inflation.Inflation caused by overheated economy may occur when the amount of currencies in circulation is larger than the critical value of inflation.For dealing with inflation generated by overheated economy,the analysis shows that the amount of currencies in circulation is less than the critical value of inflation when governments manage and control a part of amount of currencies in circulation by adopting the measures of increasing banks' deposit rates and so on,and thus the possibility of occurrence of inflation is reduced.So,governments also play an important role in preventing the generation of inflation.