What Is Nonlinear Management?

Non-linear system: A system is non-linear if its output is not proportional to its input. Mathematically, the characteristic of nonlinear systems is that the principle of superposition is no longer true. The superposition principle means that the sum of two solutions of the equation describing the system is still its solution. The superposition principle can fail in two ways. First, the equation itself is non-linear. Second, although the equation itself is linear, the boundaries are unknown or moving.

Linear refers to the proportional and linear relationship between quantity and quantity, which represents regular and smooth motion in space and time; while non-linear refers to the non-proportional and non-linear relationship, which represents irregular movement and sudden change. Such as asking: How many times the visual acuity of two eyes is one eye? It's easy to think twice, but actually 6-10 times! This is non-linear: 1 + 1 is not equal to 2. Laser generation is non-linear! When the applied voltage is small, the laser is like an ordinary electric light, and the light is scattered in all directions; when the applied voltage reaches a certain value, a completely new phenomenon suddenly appears: the excited atom seems to hear the command of "aligning to the right" and emits Monochromatic light with the same phase and direction is the laser. The characteristics of non-linearity are: cross each specialty and penetrate all fields, it can be said that it is "everywhere." For example: celestial movement has chaos; the vibration of electricity, light and sound waves will collapse into chaos; In 4 million years, the direction changed suddenly 16 times due to chaos. Even humans themselves are non-linear: contrary to traditional thinking, the EEG and heart beat of healthy people are not regular, but chaotic. Chaos is the manifestation of vitality, and the chaotic system responds to external stimuli. Faster than non-chaotic systems. It can be seen that non-linearity is around us and we can't hide from it. ^[2]

Non-essential non-linearity: Non-linearity that can be linearized using a small deviation linearization method.

Intrinsic nonlinearity: Non-linearities that cannot be solved with small deviation linearization methods.

Nonlinear System Meaning

"Linear" and "non-linear" are two mathematical terms. The so-called "linear" refers to the proportional relationship that exists between two quantities. If drawn on a rectangular coordinate system, it is a straight line. A system described by a linear function relationship is called a linear system. In a linear system, the sum of parts equals the whole. The equations describing linear systems follow the principle of superposition, that is, the different solutions of the equations are still the solutions of the original equations. This is one of the most essential characteristics of linear systems. "Nonlinear" means that the relationship between two quantities is not a "straight line" relationship, and it is a curve in the rectangular coordinate system. The simplest non-linear function is a one-variable quadratic equation or a parabolic equation. Simply put, everything is not a linear function, such as all polynomial functions higher than first power, are non-linear. A system described by a non-linear functional relationship is called a non-linear system.

Accurate non-linear testing in the system

Differences in nonlinear systems

Qualitatively speaking, there is only one linear relationship, while the non-linear relationship is ever-changing and numerous. Linearity is a special case of non-linearity. It is a simple proportional relationship. The contributions of each part are independent of each other. Non-linearity is a deviation from this simple relationship. The parts affect each other and are coupled. This causes non-linearity. The root cause of the complexity and diversity of the problem. Because of this, the independence of various factors in the nonlinear system is lost: the whole is not equal to the sum of the parts, the superposition principle fails, and the sum of the two solutions of the nonlinear equation is no longer the solution of the original equation. Therefore, we can only analyze specific problems for nonlinear problems.

The differences between linear and non-linear phenomena generally have the following characteristics:

(1) In the form of motion, linear phenomena generally appear as smooth motions in space and time, and can be expressed by functional relationships with good performance, while non-linear phenomena appear as transitions and jumps from regular motion to irregular motion;

(2) The response of linear systems to external influences is smooth and smooth, while the tiny changes of parameters in non-linear systems can cause qualitative changes in the form of system motion at some joint points. A large number of interactions existing in nature and human society are non-linear, and the linear action is just an approximation of the non-linear action under certain conditions.