Chaos theory book! ! !

Create a new science or chaos. Chaos theory is an evolutionary theory that the system suddenly changes from an ordered state to an disordered state, and it is a way and mechanism to study the formation of "random processes" in deterministic systems.

The American mathematician York and his graduate student Li introduced the name "Chaos" for the first time in the paper "Chaos in the Third Cycle" written by Li 1975. When Lorenz, an American meteorologist, studied the atmospheric flow in weather forecast in the early 1960s, he revealed two basic characteristics of chaos: unpredictability and extremely sensitive dependence on initial conditions. At the same time, he also found that the seemingly chaotic chaos still has a certain order. 197 1 year, French scientists Rolle and Torgens put forward the mechanism of turbulent solution of Naville-Stokes equation from a mathematical point of view, which revealed the path of quasi-periodic turbulence and the existence of strange attractor in phase space for the first time, which is one of the most powerful discoveries of modern science. 1976, American biologist mei first revealed the way to realize chaos through period-doubling bifurcation in the simulation study of the annual population of seasonal breeding insects. 1978, when feigenbaum, an American physicist, conducted a computer numerical experiment on Mei's insect population model again, he found two constants, called Fegenbaum constant. This has aroused widespread concern in the field of mathematical physics. At the same time, Mandelbrot described a large class of complex and irregular geometric objects with fractal geometry, which gave strange attractor a fractal dimension and promoted the study of chaos theory. In the late 1970s, scientists discovered chaos in many deterministic systems. Chaos, as a discipline, is still under discussion and has not formed a complete and mature theory.

However, some scientists spoke highly of chaos theory, saying that "chaos is the second revolution of physics". But some people think that this seems a bit exaggerated. Its application prospect needs to be further revealed. However, the study of chaos theory is closely related to synergetics and dissipative structure theory. They have the same task in the research from disorder to order and from order to disorder, so chaos theory is also a part of self-organizing system theory. In recent years, scientists have made important progress in the study of chaos control, and realized the first kind of chaos, that is, the control experiment of time series chaos. British and Japanese scientists are still experimenting with signal transmission methods that use chaotic signals to hide confidential information.

When chaos appears, classical science is over. For a long time, physicists all over the world have been looking for the natural order, but they are quite ignorant in the face of disorderly phenomena such as the atmosphere, the turbulent ocean, the sudden increase or decrease of the number of wild animals, the heartbeat and the changes of the brain. These irregular parts of nature are discontinuous and irregular, which has always been a mystery in science.

But in 1970s, a few scientists in America and Europe began to break through the chaos and find a way out. Including mathematicians, physicists, biologists and chemists, all of them are looking for all kinds of irregular phases. Physiologists have found surprising order from the chaos of human heart, which is the main cause of mysterious sudden death. Ecologists study the fluctuation of quantity, while economists try new analysis methods by mining stock price data. These insights began to emerge, leading us to the natural world-the shape of clouds, the path of lightning, the micro-winding of blood vessels and the gathering of stars.

From the ignorance of researchers to the madness of joining new science in the world. Ten years later, chaos has become a turbulent movement to reshape the scientific system, and there are conferences and periodicals about chaos theory everywhere. In the budget, the government invested more research funds in the army, the Central Intelligence Agency and the Ministry of Energy to explore the chaos, and set up a special department to deal with the income and expenditure of funds. In every university and joint research center, theorists regard chaos as a gay cause, followed by their major. In Rosa Ramos, a nonlinear research center integrating chaos and other related issues has been established, and similar institutions have appeared in various campuses all over the country.

Chaos creates different skills, such as using computers and dealing with special graphics, and capturing wonderful and subtle structural patterns under complex appearances. This new science has developed its own language, with unique technical terms-fractal, bifurcation, intermittence, period, folded towel, phase differential and smooth noodle map. Just as quarks and gluons in traditional physics are new elements of matter, for some physicists, chaos is a developing science rather than a finished product, a formation rather than an existence.

Chaos seems to be everywhere: the rising cigarette smoke bursts into a crazy smoke vortex, the flag swings back and forth in the wind, and the faucet changes from a steady drip to chaos. Chaos also appears in weather changes, traffic jams on aircraft channels and highways, and transportation and flow of underground oil pipes; No matter what media is used, all behaviors follow this newly discovered law. This experience has also begun to change the way entrepreneurs make insurance decisions. Astronomers observe the solar system and political scholars discuss the pressure of armed conflict.

Chaos transcends the boundaries of different scientific disciplines, because it is the macroscopic aspect of various systems, and it brings together thinkers from all over the world. A naval officer in charge of science budget once said to a group of mathematicians, biologists, physicists and doctors: "15 years ago, science was entering a crisis in trouble, but this fine division of labor was dramatically integrated because of chaos theory." The most enthusiastic supporters of the new science believe that there are only three works handed down from generation to generation in science in the 20th century: relativity, quantum mechanics and chaos theory. They believe that chaos has become the third great revolution of physical science in this century. Like the previous two revolutions, chaos theory overthrew the creed regarded as the standard in Newton's physics. As a physicist said: Relativity denies Newton's description of absolute space-time; Quantum theory denies Newton's dream of controllable measurement process; Chaos theory shattered Laplace's illusion about the predictability of causal determinism.

The revolution of chaos theory is suitable for the world we can see and touch, and plays a role on the scale of human beings. Daily life experiences, individuals and real scenes in the world become suitable research objects. For a long time, there is a feeling that is not often expressed publicly-theoretical physics seems to be far from human intuition about the world (for example, do you really believe that feathers and stones fall at the same speed? The story of Galileo dropping a sphere from the leaning tower of Pisa is a myth! No one knows whether a new theory will become a solid heresy or just an ordinary heresy, but for some desperate physicists, chaos theory is their new way out.

The study of chaos theory is highlighted from the backward part of the original physics category. The heyday of particle physics dominating the twentieth century has passed, and the limitations of explaining the laws of nature with particle physics terms are almost powerless to most problems except the simplest system. As far as predictability is concerned, it is one thing for two particles to race around an accelerator in a cloud laboratory and eventually collide, but it is completely different for a fluid moving slowly in a simple duct, the weather on the earth or the human head.

When the chaotic revolution continued to develop, top physicists found themselves comfortably returning to some phenomena on the human scale. They not only studied nebulae, but also began to study clouds. They have done fruitful computer research not only on the Cray supercomputer, but also on the Macintosh. First-class journals publish articles about the strange power of a ball jumping on a table, which is equal to articles on quantum mechanics. The simplest system will also produce confusing predictability problems. Nevertheless, order will suddenly emerge from these systems-order and chaos. Only a new science can connect the micro: for example, a water molecule, a heart tissue cell and a neutron; And the collective behavior of millions of macroscopic objects.

Look at the two adjacent bubbles at the bottom of the waterfall. Can you guess how far they are at the top of the waterfall? In fact, there is no trace, just as standard physics thinks, as if God secretly put all the water molecules in a black box and stirred them. Physicists usually look for complicated reasons when they see such complicated results. When they see the chaotic relationship between things entering and leaving the system, they think it is necessary to artificially add disturbances or errors and random factors to any realistic and feasible theory. Modern research on chaos theory began in the 1960s, and gradually realized that a fairly simple mathematical equation can describe a system as rough and unpredictable as a waterfall. As long as you enter a small difference at the beginning, it will soon lead to the opposite result. This phenomenon is called "sensitive dependence on initial conditions". For example, in weather phenomena, this can be interpreted half jokingly as the well-known butterfly effect-a butterfly spreading its wings in Beijing today will disturb the air and may trigger a storm in new york next month.

When the explorers of chaos theory began to recall the development of new science, they traced back to many worn-out paths in the past knowledge field. But one thing is particularly clear. For young physicists and mathematicians on the revolutionary journey, the butterfly effect is their same starting point.