| Classical economics is built on the basis of the assumption of general equilibrium, that refers to the state that the production and price of goods are decided by the market’s equilibrium which can be obtained from the theory of marginal efficiency. General equi-librium is the most important guidance to understand the complex connection between groups of equations of economics and also is the foundation of analysis of the classical economics, but its essence is a ideal model that similar to the classical physics such as the thermodynamics about isolated system, so the mathematics of general equilibrium is beautiful but not practical.Classical economics don’t tolerate the existence of disequilibrium, mutation, fric-tion or other complexity that really belongs to the world, otherwise the equilibrium can-not be achieved in mechanism. For example, disequilibrium is believed to be short-term,since the buyers and the sellers will constant correct the price and quantity to achieved equilibrium that all parties satisfied with each other. Then there are not a lot of space for the existence of disequilibrium and arbitrage. While mutation is treated as accident caused by external shocks, the internal of the system just allow some small fluc-tuations around the equilibrium to ensure the stability of the general equilibrium. The friction will lead to energy dissipation, further to the irreversible and the depends of the path, so it would have been unthinkable for classical economics. Classical economics always assumes that the system can achieve the perfect equilibrium through constant correction, and believe that the market is an "invisible hand" to promote the system to reach the equilibrium state.In this sense, the classical economics is very similar with the thermodynamic systems. In1954, through the fixed point theorem, Arrow and Debreu proved the existence and uniqueness and the stability of solution of general equilibrium, that lead to perfect combination of the equilibrium analysis and mathematical analysis. Like other subjects,the axiomatic method of economics is pop up since then,but with the price that the model is more and more away from reality, and became a academic plaything that pursuit of self consistent.In this picture, the microeconomic theory of optimization analysis and the input-output analysis are two outstanding representative of the general equilibrium. The for-mer is built by Marshall, and the latter is founded by Leontief. According to the general equilibrium theory, the price and quantity of products can eventually be determined by the solution of equilibrium, so the goal of economics is to seek the solution, and accord-ing to the optimal solution to decide the production and consumption. Therefore, the task of Marshall’s microeconomics is to analyze the micro unit how to maximize the utility of production and consumption. Due to the solution of general equilibrium in-volving thousands of goods, it will be a huge impossible work for solving the equations, that cause Marshall propose the local equilibrium theory to simplify the problem. The input-output analysis is another specific extension of the general equilibrium, whose purpose is to empirically study the complex interdependent relationship between goods.But a lot of economic phenomenon shows that the theory of general equilibrium is deviated from actual economic conditions. Lots of non-equilibrium phenomenon in economy,such as dissipation,self-organization, criticality, and adaptive, can’t be ex-plained by the theory framework of general equilibrium. Especially after the rise of the complex system science, nonlinear science, self-organization theory, and the biological evolution theory, the economic system be treated as a complex system is apparent. But, because of lack of mathematical analysis, complexity of economics are still excluded from the mainstream economics.In order to make up the obvious defects, orthodox e-conomics attempts to relax the assumptions through replace the general equilibrium by the dynamic equilibrium. But the dynamic equilibrium still can not explain the complex adaptive features of the economic system.After the rise of theory of complex network, the study on economic system,through the complex network model, has entered a new position. As a natural network,the input-output system is a perfect intersection between complex network science and economics. But the present way of complex network research on input-output system is just limited to analysis about network’s topology structure.Although it has got many meaningful re-sults,but still have not a breakthrough in ideas. This article emphasizes the input-output system itself is a flow network, highlight the openness of flow characteristics, break the picture of circulation of value of the general equilibrium, and attempt to combine some complex features such as dissipation, growth,self-organization criticality with the input-output network, to explore the complexity of economics. In a word, through the study on the dissipation, evolution, critical features of input-output flow network, a complexity economics may be approved by people.The article is organized as follows:first, we treat the input-output system as a flow network and analyze the dissipation structure characteristics of this flow network. We found that the more mature of the economic system, the higher efficiency of energy and material consumption.As to the allometric scaling of this flow network, we built the calculation method of metabolic rate of input-output flow network and get the allometric scaling exponent is0.819,that contrast with the3/4law of biological systems, suggesting that economic system completely have characteristics of complex system such as living organisms.Secondly, after statistics,we found some scale-free characteristics about the input-output network, and in order to explain this phenomenon, we made a mathematics mod-el. This model ask for the innovative features and the emergence of system to meet the observed index that is unthinkable in the equilibrium economics.In the third, we discusses the self-organization criticality of input-output flow net-work, and make two self-organized critical model for input-output flow network.By evidence of U.S. economic cycle, on the medium level, we think the economic system is a critical edge system.Finally, we summarize the successes and failures of the study and think the future research should focus on non-equilibrium fluid economics.This paper is a try to adopt method of complex system to research input-output system, which have some innovation in methods and results, but also face many short-ages. We hope this inadequate study can contribute to the complexity economics.
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