Multi-Resolution Modeling (MRM) And Aggregation In Complex Systems And Its Application

T he simulation and optimizing control for large-scale complex systems are depended on the models which can describe the system's hierarchical organization structure and dynamic behavior appropriately and accurately. There are many kinds of data (quantificational, quasi-quantificational, qualitative) when simulating and modeling for complex systems. These datas reflect the behavior from different levels and aspects and they always describle the systems in different granularity and resolution. At the same time, in view of some deficiency of traditional modeling methods, a new approach to system modeling梞ultiresolution modeling and aggregation/disaggregation梙as been developed since 1980's,and is now being used in the simulation and optimizing decision-making for large scale complex systems.In this paper, the characteristics of the large-scale complex systems and their hierarchical embodying relationships are discussed at first. Then, the advantages of Multi-Resolution Modeling(MRM) over the traditional modeling methods are view in details in the first chapter ,and in the 2nd chapter, some important concepts such as variable granularity analysis.aggregation and disaggregation.smooth and consistency transformation between different resolution models are studied so as to propose certain implementing approachs.Thereupon, in the 3rd chapter, the characteristics of the ecological systems are discussed and the necessity of aggregation is proposed, then, the method of choosing macro-variables isdiscussed ,and the aggregation method for the systems of ordinary differential equation is proposed .In the 4th and 5th two examples: the model of single population and the model of two populations in different environment are discussed, the method which have proposed in 3rd chapter is implemented in the two examples.The aggregation method reduces the dimension and the complexity of the micro-system, but the aggregation model is not the copy of the micro-system,so it makes new global properties emerge at the macro-level which is called emergence. In this paper, the concept of the functional emergence and the dynamical emergence are defined. The direction of emergence effect is bottom-up , and there also exists top-down effect which is called immergence. These two effects are compared and analyzed in the 6th chapter.