Numerical Simulation-Based Model for Analyzing the Correlation between GDP Index and Quality of Life

As the information carrier of the social economy, the quality of statistical data has become more concerned and sensitive in the society and the data quality of GDP, as one of the core aggregate indicators of national economic accounting, has received more extensive attention. Government statistical departments have placed data quality in a strategic position in the development of statistical undertakings, and the assessment of GDP data quality is an important part of their data production management process. This paper uses the livelihood index to represent the survey data of quality of life level and theoretically analyzes and empirically tests the importance of improving quality of life in the current development stage, the relationship between improving people’s livelihood and economic development, and the population distribution of public service satisfaction and the influence of public service satisfaction on life satisfaction. In response to the major real-life problems in the development of economic and social quality of life, many research institutions have carried out in-depth survey and research work at various levels and in various fields, with large samples and a wide range, accumulating a large number of survey and research reports with detailed data and unique content, the same as thematic research reports with standardized analysis based on survey data. Taking mathematical economics as the basic starting point, this paper conducts an in-depth study on the relationship between GDP index and quality of life from the analysis of the operation law, inner operation mechanism, stability, and other relevant aspects of the model itself. Taking the classical endogenous economic growth model as the starting point, the endogenous theoretical nonlinear dynamical system of GDP index and quality of life, the nonlinear dynamical system of GDP index and quality of life, and the theoretical nonlinear system of GDP index and quality of life supply and demand are constructed; and the stability analysis is conducted for the constructed nonlinear dynamical system, the situation when the model starts to destabilize is discussed and the model is addressed. The theoretical analysis and numerical simulation results are presented for the conditions of existence, bifurcation direction, and stability of the bifurcation period solution of the Hopf bifurcation that may occur.