Implementation of the Dynamical System of the Deposit and Loan Growth Based on the Lotka-Volterra Model and the Improved Model

摘要

The Lotka-Volterra model is a very popular mathematical model based on the relationship in Ecology between predator, which is an organism that eats another organism, and prey, which is the organism which the predator eats. Predator and prey evolve together. The prey is part of the predator's environment, and the existence of the predator depends on the existence of the prey. As a dynamical system, this model could generate limit cycles, which is an interesting type of equilibrium sometime in the system of two or more dimensions. In [1,2], the dynamical system of the the Deposit and Loan Volumes based on the Lotka-Volterra Model had been developed. In this paper, we improve the definition of parameters in the model and then implement the model on the data of banking from January 2003 to December 2014 which consist of 4 (four) types of banks. The data is represented into the form of return in order to have data in a periodical-like form. The results show the periodicity in the deposit and loan growth data which is in line with paper in [3] that suggest the positive correlation between loan growth and deposit growth, and vice-versa.