ANALYSIS OF THE COOPERATIVE LOTKA-VOLTERRA MODEL IN THE CASE OF TWO AUTOMOTIVE INDUSTRIES IN INDONESIA

Abstract

The automotive industry sector is one of the main sectors contributing to the national economy. Companies in the automotive industry work together to increase productivity and win the market competition. This research aims to construct the cooperative interaction between two companies into the cooperative Lotka-Volterra model. The cooperative Lotka-Volterra model was analyzed for stability at the equilibrium point and bifurcation analysis was performed. Sales data for the Calya 1.2 G product from PT Toyota Motor Manufacturing Indonesia and sales data for the New Sigra 1.2 R MT product from PT Astra Daihatsu Motor are applied to the model. The results of the study show that there is a model that explains the cooperative interaction of the two companies, namely the cooperative Lotka-Volterra model. Four equilibrium points are obtained with three equilibrium points being unstable and the fourth equilibrium point being stable with conditions. The Hopf bifurcation analysis of the model shows that there are no parameters that cause a change in stability from initially stable to unstable. The data simulation shows that the cooperation of the two companies is mutually beneficial because it increases the number of sales and creates balanced market conditions.