Types of application fields: ecological model, traffic model, environmental model, combat model, social model, medical model, mechanical model, etc.

Mathematical methods of establishing models: geometric model, network model, operation model, stochastic model, etc.

Types of modeling purposes: description model, analysis model, prediction model, decision model, control model, etc.

The types of understanding degree of model structure: white box model, gray box model and black box model.

Requirements for establishing mathematical model:

1, true and complete.

(1) truly, systematically and completely reflect the objective phenomenon;

(2) It must be representative;

(3) Extrapolation, that is, the information of the prototype object can be obtained, and the reasons about the prototype object can be obtained in the process of model research and experiment;

(4) It must reflect the various achievements made in completing the basic tasks and must be consistent with the actual situation.

2. Concise and practical. In the process of modeling, we should reflect the essential things and their relationships, and eliminate the non-essential things that have little influence on reflecting the objective truth, so that the model can be as simple and operable as possible and the data can be easily collected while ensuring a certain accuracy.

3. adapt to change. With the change of related conditions and the development of people's understanding, we can adapt to the new situation well by adjusting related variables and parameters.