The difference between linear and nonlinear

The difference between linear and nonlinear is as follows:

Nonlinear:

Nonlinear, that is, the mathematical relationship between variables, is not a straight line but a curve, surface or uncertain attribute, which is called nonlinear.

Nonlinear is one of the typical characteristics of complexity in nature. Compared with linearity, nonlinearity is closer to the essence of objective things and is one of the important methods to quantitatively study and understand complex knowledge. Any relationship that can be described by nonlinearity is generally called nonlinear relationship.

What is linearity:

The definition of linearity is generally carried out from two interrelated angles: First, the superposition principle holds that: "If ψl and ψ2 are two solutions of the equation, then aψl+bψ2 is also one of its solutions, in other words, the superposition of two states is still one state."

The superposition principle means that there is no nonlinear interaction between subsystems of the studied system.

Secondly, the functional relationship between physical variables is a straight line, and the rate of change between variables is constant, which means that the slope of the function exists everywhere and is equal in its definition domain, and the proportional relationship between variables is symmetrical in the whole definition domain of variables.

* * * Sex

Although the nonlinear relationship is ever-changing, there are still some * * * characteristics different from the linear relationship.

The linear relationship is independent, and the nonlinear relationship is interactive. It is this interaction that makes the whole no longer simply equal to the sum of parts, but may have gains and losses different from "linear superposition".

The generation of laser is nonlinear. When the applied voltage is small, the laser is like an ordinary electric lamp, and the light scatters in all directions. When the applied voltage reaches a certain value, a new phenomenon will suddenly appear: the excited atoms seem to hear the command of "align to the right" and emit monochromatic light in the same phase and direction, that is, laser.