Fixed point of discrete dynamical system of Lotka Volterra model

Abstract

Fixed point theorem is one of the theories in mathematics that has make many proofs been in existence. Lotka-Volterra model is a widely used pair of first-order nonlinear differential equations used to interpret the dynamics of two species that is a predator and a prey. The paper employs the contraction mapping and the Banach Fixed point theory on the Discrete Dynamical type of the LotkaVolterra to see the outcome of its behavior. The Banach Fixed Theory is used in determining the fixed point of discrete dynamical system of Lotka Volterra model. The following solutions (0,0),  have all be discovered and they are fixed points of Lotka Volterra Model. The fixed point serving as the limiting behavior of Lotka Volterra is continuous and convergent.