Linear relation and nonlinear relation

Linear linear, which refers to the relationship between quantity and quantity in proportion, straight line, and represents rule and smooth motion in space and time;

Nonlinear non-linear refers to the non-proportional, not linear relationship, which represents irregular motion and mutation.

Linear: The relation between the quantity and the quantity, which is proportional and linear, can be understood mathematically as the function of the first order derivative as the constant;

Non-linear: Refers to the relationship of not proportional, non-linear, the first derivative is not constant.
Linear relationship:

There is a quadratic function relationship between the two variables, it is said that there is a linear relationship between them. Positive proportional relation is a special case in linear relation, and inverse proportional relation is not linear relation. More generally speaking, if the two variables as the horizontal and vertical axis of the point, the image is a straight line on the plane, then the relationship between the two variables is a linear relationship. That is, if a two-yuan equation can be used to express the relationship between the two variables, the relationship between the two variables is called a linear relationship, and therefore, the two-Yuan equation is also known as linear equations. By and large, the one-time equation with n variables, also known as n-ary linear equations, has nothing to do with straight lines (in fact, this is the concept of hyper-plane).
Linear:

A linear equation is also called the first time. An equation in which the unknowns are all at once. Its general form is ax+by+...+cz+d=0

Nonlinear relationship:

Nonlinearity refers to the mathematical relationship between two variables, not a straight line, but a curve, surface, or indeterminate attribute, which is not a simple proportional (linear) relationship. Nonlinearity is one of the typical properties of nature's complexity; compared with linear, nonlinear is more close to the nature of objective things, and it is one of the important methods to quantify and understand complex knowledge.

Nonlinear equations:

Nonlinear equations are compared to linear equations, which are equations with higher order term, and the first derivative is not a constant equation group.

Commonality

Although the nonlinear relationship is changeable, it has some similarities with different linear relations.

Linear relationships are unrelated independent relationships, and nonlinearity is interaction, and it is this interaction that makes the whole no longer simply all equal to the sum of the parts, and may appear different from the "linear superposition" of gain or loss.

The generation of lasers is nonlinear. When the applied voltage is small, the laser is like an ordinary electric light, scattering in all directions, and when the applied voltage reaches a certain value, a new phenomenon occurs suddenly: the excited atoms seem to hear "right-to-starboard" commands, emitting monochromatic light that is consistent in phase and direction, or laser.

so far, there is no clear and complete understanding of the non-linear concept and non-linear nature, and the philosophical significance of it has not been fully excavated.