An open system always has an exchange relationship between matter and energy with the external environment, and the specific process that constitutes this relationship can be physical, chemical or even a life process. Because different motion processes follow different dynamic principles, it is very difficult to sort them out in a system dominated by many processes. Especially in nonlinear systems, the state of any point is the result of many factors or many motion processes at that point. Therefore, system science puts forward a general processing method. This method is to temporarily abandon the specific form of material movement, focus on the relationship between the system and the external environment, and use input, response and output to explain the causal relationship between them or establish a mathematical model.

(1) input

From the external environment of the system, the function of changing the internal state of the system is called input.

If there are multiple forms of actions from outside the system, they can be expressed by multiple inputs. If there is only one, it can be called single input. An input is often a time series of a signal, and the size of the input can be expressed by the physical quantity of the action or the degree of a certain state scale, that is, the signal.

(2) Response

Under the action of input, the internal state of the system is called the response of the system.

The entity system is composed of various elements (substances), and any input may lead to the result of system comprehensive dynamics, forming a new polymorphic combination, that is, multi-response. Each response can be represented by a corresponding physical quantity or state scale, that is, a response signal. The response process is represented by the time series of response signals.

(3) Output

Because of the input excitation, the system will respond to the external environment, and this influence from the system is called the output of the system.

Similar to input, output can also be divided into multi-output and single output, and the process of output is recorded by the corresponding signal time series.

Signal is the carrier of information, and the time series of input, response and output signals contains a lot of information about the movement and structure of things and energy in the external environment and system.

The extraction of information is mainly realized by analyzing the meaning of the signal itself and two characteristics in the time series. Signals are symbols, also known as "codes", such as sound codes and electric codes, which can usually be understood as a series of digital symbols used by people to describe the size, characteristics and conditions of objective objects. On the surface, it doesn't mean anything. For users, it has content, which may represent the size of groundwater head in a certain place, the concentration of some components of water quality, or the indication of surrounding rock pressure or temperature at a certain depth. In addition, the extraction of information also needs to cooperate with the analysis of two characteristics of signal time series, one is the order of numbers in time series; The second is the statistical characteristics of numbers in different time periods, that is, the changes of mean and variance. For example, in the outdoor temperature time series of more than one year, the temperature changes are ups and downs, but it can be found that the temperature has an upward trend in a certain time period and a downward trend in another time period, so it can be judged that the former may be spring and the latter may be autumn. The reason for this judgment is the temperature significance of numbers, and the arrangement characteristics of daily temperature in time are consistent with our existing understanding of seasonal division. It can also be found that the temperature change trend is not obvious in a certain period of time, but its mean value is large and its variance is small; In another time period, the average value is smaller and the variance is smaller. It can be inferred that the former is about summer and the latter is about winter. This judgment obtained by analyzing the statistical characteristics of digital time series is also consistent with our feelings.

The above example may be too simple, but we can learn the basic methods of information extraction from it. According to this method, many important information hidden in the time series of input signals can be revealed, such as the type and intensity of external environment acting on the system, the continuity of the mode of action, the frequency (period) of action and its frequency spectrum. As for the response signal time series, it can provide a lot of information about the system, including the system's ability to respond to external influences, adaptability and self-adjustment. The time series of output signals reflects the response of the system to the external environment, including the form, size and functional behavior of material and energy output.