Abstract: The co-evolution analysis is critical for managers to understand the internal mechanism of composite system, without exception to financial system with insurance, banking and stock markets. There are only few researches on the issue of the composite system with two subsystems using time series, and how to assess the dynamic relationship of the composite system with three or more subsystems is underestimated. Especially, the lag effect across different subsystems is very common in the real world, and some economic and management policy as well as major events have remarkable effects on the operation of composite system. Furthermore, considering the fact that the sample in time series is always ineffective to estimate the coefficients in the co-evolutionary equation, it is necessary to propose a new method which can be applied to panel fata. To overcome the three drawbacks, in this paper, a general framework is built.
Based on the theoretical analysis of the linkages among insurance, credit and stock markets, combining synergistic theory and the improved PSO based on dynamic neighbor topology and local search (DNLPSO), a dynamic co-evolution model is proposed for analyzing the development process of three opening multiplexed system. The computation method for order degree is constructed on the basis of DEAHP, and then the corresponding computational approach is given based on DNLPSO algorithm. Further, the stability analysis of the new co-evolutionary model is given. With the nonlinear relationship among differentsubsystems taken into consideration, the parameters of structural change and lag structures depict the impact of major events and lag effects. Using provincial penal data, the empirical study of coordination evolves in insurance, credit and stock composite systems covering 2004-2013 is unfolded. Results indicate that this model reflects the effects of lag structures and the 2008 financial crisis well, and manifests this complicated system's partial relevance and the whole evolution trends stable completely, and puts forward a basic paradigm for empirical analysis on co-evolution of three composite systems.

Key words: dynamic co-evolution, stability analysis, DNLPSO algorithm, composite system