Modeling Of Species Interaction in a Habitat Using Lotka- Volterra Type Systems

Mathematical models have been useful in the area of modeling of real life situations; its application can be found in virtually all spheres of scientific researches. As such, we adopt its use in the field of ecology where preys have to compete with other prey for survival. In this paper, we considered Lotka-Volterra type systems, consisting of two first order differential equations which were used to model the population size of prey–predator interaction. We also proposed a system of first order differential equations to model the population sizes of a prey and two predators. Under these conditions one of the predators dies out while the remaining predator and prey approach periodic behavior as time increases. Also we model the population size of two preys and one predator where there may be interaction between the preys. Under these conditions we found that one of the preys died out while the remaining preys and predators approached periodic behavior as time increased. For critical cases, each positive solution of the system was seen to be periodic in nature. Various examples and results were presented and further study was proposed.