Firstly, the mathematical model is established, and the corresponding simplification and assumptions are made according to the purpose and requirements of the problem. Then the differential equation is listed according to the law, and the solution of the equation is obtained; Finally, the actual object is brought into the result, and the problem is described, analyzed, predicted and controlled.

Because natural resources, environmental conditions and other factors have a blocking effect on population growth, and with the increase of population, the blocking effect is getting bigger and bigger, so the growth rate will decline after the population grows to a certain amount.

The blocking effect is reflected in the influence on the population growth rate, which makes it decrease with the increase of population. If expressed as a function, it should be a subtraction function, so equation (2.2) is rewritten as (2.7). One of the simplest assumptions of is that is set to the linear subtraction function of, that is, (2.8).

This is called the inherent growth rate, which means the growth rate when the population is small (theoretically). In order to determine the meaning of the coefficient, the maximum population that can be accommodated by natural resources and environmental conditions is introduced, which is called population capacity.

Thinking method:

Mathematical modeling is a mathematical thinking method, and it is a powerful mathematical means to describe and "solve" practical problems by using mathematical language and methods through abstraction and simplification.

Mathematical modeling is a process of describing actual phenomena with mathematical language. The actual phenomena here include both concrete natural phenomena, such as free fall, and abstract phenomena, such as customers' value tendency to a certain commodity. The description here includes not only the description of external form and internal mechanism, but also the prediction, experiment and explanation of actual phenomena.

We can also intuitively understand this concept: mathematical modeling is a process that makes pure mathematicians become physicists, biologists, economists and even psychologists.

A mathematical model is generally a mathematical simplification of actual things. It often exists in an abstract form close to the real thing in a sense, but it is essentially different from the real thing.

There are many ways to describe an actual phenomenon, such as recording, video recording, metaphor, rumors and so on. In order to make the description more scientific, reasonable, objective and repeatable, people use a generally accepted strict language to describe various phenomena, which is mathematics.