Grey Lotka–Volterra model and its application

The aim of this study is to analyze the long-term relationship between the two variables and to predict the values of two variables in the social system or economic system. Based on the grey modeling method, a grey Lotka–Volterra model is proposed, and a linear programming method is used to estimate the parameters of the grey Lotka–Volterra model under the criterion of the minimization of mean absolute percentage error (MAPE). The obtained simulation results have been verified by three cases: the study of research and development investment (R&D) and gross domestic product (GDP), the study of fixed assets investment (FAI) and the (CPI), the study of energy consumption and the GDP. Comparisons of the obtained results with the traditional grey model demonstrate that the grey Lotka–Volterra model is able to analyze the relationship between the two variables and predict the values of these variables effectively.

► We explain the economic meaning of accumulation from grey system. ► Grey Lotka-Volterra model are presented. ► Grey Lotka-Volterra provides comparable results with other widely accepted methods.