Research characteristics of complex systems
1987, Craig Reynolds of Los Angeles symbolics corporation exhibited a computer model at an artificial life seminar, which randomly put several bird models into a screen environment full of walls and obstacles. Every "bird" follows three simple rules: 1: It tries to keep the minimum distance from other obstacles, including other "birds". It tries to keep the same speed as its neighbor "bird". 3. It tries its best to move to the gathering center of neighboring groups. The result of every operation of this model is that "birds" gather in groups. Sometimes, these "birds" can even be divided into smaller groups, fly over both sides of the obstacle, and then reunite from the other end of the obstacle. These rules don't say that, just give instructions to each individual "bird". From this point of view, every complex system has some motivation, which makes the simplest bottom rules produce extremely complex behaviors, but these behaviors are far from deterministic and unpredictable chaos. The structure of fractal graphics is complex, and it is always entangled in it indefinitely, but it is miscellaneous and not chaotic, and it has internal order and self-similar structure. In fact, complex systems are not unpredictable, but can predict the future. Complex systems not only have some characteristics of chaos, but also have the characteristics of transcending chaos:
1: Many interactions that produce complex behaviors make each system as a whole spontaneously self-organize. "Baird" cluster, atoms find the smallest energy state by combining with each other. The economic system established by human beings to meet their own material exchange needs, and so on. In all these cases, individual drivers seek mutual satisfaction, and at the same time obtain many comprehensive characteristics that individual drivers can never have;
2. These complex self-organizing systems can adjust themselves. Baird's team flew over both sides of the obstacle in small groups, and then regrouped from the other end of the obstacle. Human beings are constantly learning in contact with the world, and the human brain is also constantly strengthening or weakening countless relationships between neurons. The law of value in economy is that price fluctuates with value, but the long-term overall result tends to be balanced;
3. All complex systems can predict the future. The "bird" will be divided into smaller groups when encountering obstacles, but the previous gathering state shows that it will still gather again. Long-term economic recession will reduce people's consumer confidence, which in turn indicates that the economy will further decline. From tiny bacteria to all organisms, their genes contain predictive codes to adapt to new environments that have never appeared before.
1, complex system
1. 1 the basic concept of complexity
There is no unified statement about the concept of complexity. Because complexity covers a wide range, there are 489 titles containing the word complexity in the bibliographies of the Library of Congress 1975 to1February 1999 15. It involves algorithmic complexity, computational complexity, biological complexity, ecological complexity, evolutionary complexity, developmental complexity, grammatical complexity, and even economic complexity and social complexity. It should be noted that a considerable part of "complexity" in the field of social science refers to chaos, heterogeneity and repetition, rather than "complexity" associated with chaos, fractal and nonlinearity in the field of scientific research. Because the concept of complexity has different research objects and analysis methods in different disciplines, the definition of complexity is also different. So far, there is no strict definition of complexity.
1.2 Several concepts related to complexity and their relationships
(1) Randomness: Random phenomenon is the representation of uncertain system connotation and definite extension.
An important achievement of complexity research in recent years is that randomness is not complicated (although some people say that randomness is the greatest complexity). In fact, many definitions of complexity in history are aimed at randomness. Complexity is between randomness and orderliness, which is an irregular combination of structure and orderliness on a random background.
It has been proved that a system containing both chaos and random phenomena will be dominated by nonlinear mechanisms rather than random factors with the evolution of time.
(2) Fuzziness: Fuzziness is a manifestation of the system's definite connotation and uncertain extension. Fuzzy mathematics can be used to reduce the uncertainty of extension. Obviously, this is essentially different from the research of complexity science.
(3) Simplicity and complexity
Simplicity has always been a guiding principle of modern natural science, especially physics. Many scientists think that the basic laws of nature are simple. Einstein is an outstanding representative of this view. Although complex phenomena abound, people still try to simplify them into simpler components or processes. Of course, there are many complicated things or phenomena, and there are simple laws or processes behind them. However, on the other hand, there are many things and phenomena that cannot be dealt with by simple reductionism.
1.3. Basic characteristics of complex system definition
Due to the different definitions of complex systems, there are at least 30 kinds, and their representative features are as follows:
(1) A complex system is a chaotic system (chaos school).
(2) An adaptive evolutionary system (Santa Fe).
(3) Multi-agent hierarchical system.
(4) A system including a feedback loop.
(5) John Warfield, whose behavior cannot be explained by traditional theories and methods.
(6) Dynamic nonlinear system.
(7) The new behaviors and relationships (the definition of ontological complexity) that are irreducible after a certain movement or behavior crosses the level. Ontology complexity can also be divided into: (catastrophe theory and chaos) motion complexity and (fractal and unstable) structure complexity. All have cross-level characteristics. Its characteristics are nesting, mutual connection, mutual influence and joint action.
(8) Effective understanding and expression of objective complexity (complexity definition of epistemology). The concept of complexity in the epistemological sense also summarizes various concepts and meanings of complexity defined by description length in natural science and technical science, especially the meaning of "effective complexity".
2. Complexity science
2. 1 Scientific definition of complexity
Complexity science is a science that uses non-reductionism to study the mechanism and evolution law of complexity in complex systems.
2 .2 Research object of complexity science
Anderson pointed out that complexity research should not be "premature and rash" when trying to establish an all-encompassing framework like general semantics or general system theory; Instead, we should focus on concrete and testable mechanisms and concepts.
As the research object of complexity science, Santa Fe Institute runs through various ideas, such as symmetry breaking, localization, fractal and strange attractor.
However, several popular books with similar titles published in the early 1990s all regarded complexity research as a science between order and chaos.
Complex system is the object of complexity science research.
2.3 the basic principles of complexity science
(1) integrity principle. Because the research object of complexity science is nonlinear economic system, the traditional superposition principle is invalid. Therefore, the research object can not be divided into several small systems and then superimposed, and the whole economic system can only be grasped as a whole. This is also in line with the idea of system science.
(2) Dynamic principle. Complex systems must be dynamic systems, that is, systems related to time variables. Without the change of time, there would be no evolution of the system, and there would be no law of complexity. Because "things always develop and change".
(3) the principle of unity of macro and micro. Complexity science believes that the large fluctuation of macro variables of the system may come from the small changes of some elements that make up the system. Therefore, in order to explore the changing law of macro variables in complex systems, it is necessary to study its micro-mechanism. However, due to the nonlinearity of the mechanism, the system cannot be decomposed, so it needs the unity of macro and micro.
(4) The principle of unity of certainty and randomness. The theory of complexity science shows that stochastic behavior process can appear in deterministic economic system, which is a manifestation of the "internal" randomness of the system, which is essentially different from the irregular results of nonlinear systems with external stochastic terms. For complex systems, the structure is certain, the short-term behavior can be accurately predicted, and the long-term behavior becomes irregular. A small change in initial conditions will lead to a huge deviation in the running trajectory of the system. For a nonlinear economic system with external stochastic terms, the evolution rules of the system are always uncertain, so neither long-term behavior nor short-term behavior can be defined.
3. Problems in complexity science research
(1) Scientific research should start from the analysis of facts, not from the definition.
(2) In essence, complexity is a science about process rather than state, and it is a science about evolution rather than existence.
(3) complexity science research should not be too broad and all-encompassing.
(4) The scientific research of complexity should establish corresponding scientific norms to make the research of complexity "evolve" healthily.
4. Key research fields and problems of complexity science in China.
(1) The basic theories and methods of complexity science mainly include:
The basic connotation and concept of complexity science;
Complexity measurement methods, identification and evaluation methods of complex systems;
Theory and method of complex system control;
Evolution and emergence mechanism of complex systems;
Data mining technology of complex system;
Evolutionary calculation method of complex system;
Simulation technology and platform of cellular automata and complex system;
Complex system integration seminar hall method, etc.
(2) The complexity of physical (natural) systems mainly includes:
Complexity of material damage, breakage and mutation;
Complexity of dynamic system of metallogenic evolution;
Complexity mechanism of turbulence;
Complexity of aerodynamic system and complexity of weather forecast;
Control method of physical chaotic system;
Complexity of disasters.
(3) The complexity of life system mainly includes:
Complexity of human meridians based on TCM theory;
Cognitive complexity of the brain;
Complexity and diagnosis of human heart and brain diseases;
The complexity of ecosystem evolution is worth studying.
(4) The complexity of social and economic management system mainly includes:
Complexity of financial system;
Chaos economics theory and method;
Management theory and method based on complexity science;
Complexity of economic system evolution;
Control and management methods of disaster complexity;
Management complexity based on network system;
Modeling, control and management of complex social systems.