Kajian Model Lotka-Volterra dalam Dinamika Persaingan Pasar

Abstract

The Competitive Lotka–Volterra mathematical model describes the interaction and competition between two market shares represented through a system of ordinary differential equations. The model incorporates a limiting factor in the form of carrying capacity to ensure that the growth and decline rates of sales for both products do not occur exponentially. The analysis results indicate that the inclusion of carrying capacity constraints allows the system to achieve stability conditions at certain equilibrium points, with parameter values significantly influencing changes in sales levels. Through the formulation and analysis of the competitive Lotka–Volterra model between Calya and Sigra, three equilibrium points were obtained, representing stable system condi tions. The eigenvalue analysis for each equilibrium point using the Jacobian matrix shows that the system does not experience a zero-sales condition, as both products maintain intrinsic growth rates. This finding suggests that the competitive interaction between Calya and Sigra plays a vital role in determining the dynamics of sales varia tions within each market player. Despite competition, each product retains its ability to sustain through its intrinsic sales growth potential. In summary, the developed Lotka Volterra model can serve as a theoretical foundation for analyzing market competition dynamics and for formulating optimal and sustainable sales strategies