Abstract: This paper introduces two concepts named “concentration of knowledge” and “speed of knowledge application”, and uses system dynamic equations of knowledge dilution effect to explain the mechanism of knowledge spillovers. Meanwhile,the research analyses the characteristics of knowledge spillovers mutations from the perspective of catastrophe theory,and uses the method of substitution to transform the system dynamic equations referenced on the catastrophe theory, then sets up the cusp catastrophe model for state of knowledge spillover, and discusses the criterion rule between the changes of control factors in the knowledge dilute system and the state of knowledge spillovers,and illustrates knowledge spillovers features in knowledge application process such as a sudden jump, hysteresis effect and the changing mechanism of cusp catastrophe between knowledge accepting and knowledge spillover. Finally,the paper makes an empirical research by using the panel data of 31 provincial-level administrative region of China, and indicates the knowledge spillover state and change and the development trend taking each province as a whole, which provide some use for reference to the local economic development and knowledge strategy decision.

Key words: knowledge application, knowledge spillover, cusp catastrophe, state identification

摘要： 本文引入“知识浓度”和“知识应用速度”两个概念,利用知识稀释效应的系统动力方程解释知识溢出机理。从突变视角分析了知识溢出的突变特性,借鉴尖点突变理论对系统动力方程进行换元变换,建立了知识溢出状态的尖点突变模型,讨论了知识稀释系统控制因子的变化与知识溢出状态间的判定规则,说明了知识应用过程中知识溢出特性如突跳、滞后效应等特性及知识溢出态和接受态之间转化的尖点突变机理。最后,利用我国31个省级行政区面板数据进行实证研究,揭示以省级行政区为对象的知识溢出状态、变化情况及发展趋势,为我国区域经济发展和知识战略提供理论指导。

关键词: 知识应用, 知识溢出, 尖点突变, 状态判别