The practical problems are abstracted into mathematical symbols and formulas, so that the problems can be quantitatively analyzed and solved. At present, mathematical models are widely used in scientific research, economic management, social policy and other fields. Next, the classification and characteristics of mathematical models will be introduced in detail.

1. Static model and dynamic model

According to different time factors, mathematical models can be divided into static models and dynamic models. Static model refers to the model established at a relatively fixed time point, while dynamic model is a model established for the problem of time flow. Static model is more suitable for simple problems, and dynamic model is more suitable for problems that need to consider time factors.

2. Deterministic model and stochastic model

According to the degree and randomness of variables, mathematical models can be divided into deterministic models and stochastic models. Deterministic models generally assume that all parameters are determined and are not affected by random factors, such as linear programming model and polynomial fitting model. Stochastic model involves the category of probability statistics, including stochastic process, Markov model, Monte Carlo simulation and so on.

3. Nonlinear model and linear model

According to the functional relationship between variables, mathematical models can be divided into two types: nonlinear models and linear models. The characteristic of linear model is that the relationship between variables can be expressed by simple linear equations, such as linear function and quadratic function.

The characteristic of nonlinear model is that the functional relationship between variables is not linear and cannot be expressed by simple linear equations. This model includes exponential function, logarithmic function and trigonometric function.

4. Discrete model and continuous model

According to the value of variables, mathematical models can be divided into discrete models and continuous models. Continuous model means that the values of variables are uniform and continuous in a certain range, such as derivatives and integrals in calculus. Discrete model means that variables can only take finite or discrete values, such as network shortest path problem, integer programming problem and so on.

5. Static description model and dynamic process model

Mathematical models can be divided into static description model and dynamic description process model according to the time factor of describing a given object. Static description model is used to describe the state or object existing at a certain moment, such as flow balance equation, income statement, etc. The dynamic description process model focuses on the evolution relationship of the changing process, such as difference equation, differential equation and dynamic programming.

To sum up, mathematical model is a tool to abstract practical problems into mathematical symbols and model forms for quantitative analysis and problem solving. There are many kinds of mathematical models, so it is necessary to choose the corresponding types of mathematical models to model and analyze according to the characteristics, needs and conditions of the problem, so as to better solve the practical problems.