ANALYSIS OF COMPETITION BETWEEN TWO RETAILERS USING LOGISTIC PREY-PREDATOR MODEL WITH FUZZY INITIAL CONDITION

The interaction of prey and predator species is a biological process with profound ecological implications that occurs all over the world. The dynamics of Prey-Predator is used for modelling competition in industry, finance and business etc. In this article, we employ a logistic Prey-Predator model to explain competition between the two retailers. While modelling such problem, collecting parameters and/or initial conditions may imprecise so, fuzzy theory gives more realistic depiction. We solve this nonlinear model taking initial condition fuzzy using Fuzzy Laplace transform technique and give closed form fuzzy solution. We also give the existence of fuzzy solution and condition for stability of the system. Lastly, a numerical illustration is solved and compared at core. KEYWORDS: Logistic Prey-Predator model, Nonlinear differential equations, Triangular Fuzzy Number, Modified Hukuhara derivative, Stability analysis, Taylor's theorem MSC: 34A07 La interaccion de las especies presa y depredadora es un proceso biologico con profundas implicaciones ecologicas que ocurre en todo el mundo. La dinamica Prey-Predator se utiliza para modelar la competencia en la industria, las finanzas y los negocios, etc. En este articulo, empleamos un modelo logistico Prey-Predator para explicar la competencia entre dos distribuidores minoristas. Al modelar dicho problema, la recopilacion de parametros y/o condiciones iniciales puede ser imprecisa, por lo que la teoria difusa brinda una descripcion mas realista. Resolvemos este modelo no lineal tomando la condicion inicial difusa usando la tecnica de transformada difusa de Laplace y damos una solucion difusa de forma cerrada. Tambien damos la existencia de solucion difusa y condicion de estabilidad del sistema. Por ultimo, se resuelve una ilustracion numerica y se compara en el nucleo. PALABRAS CLAVE: modelo logistico presa-depredador, ecuaciones diferenciales no lineales, numero borroso triangular, derivada de Hukuhara modificada, analisis de estabilidad, teorema de Taylor