On the Comparison of Stability Analysis with Phase Portrait for a Discrete Prey-Predator System

摘要

Prey-predator interaction can be defined as consumption of predator against prey. It is well known that when the predator absent, the growth of prey population will increase. In the absence of prey, the predator population goes extinct. In this paper, we consider the interaction between prey and predator in a discrete prey-predator system. For this system, we would like to study the dynamic behavior of solutions (or in particular fixed points) for this system. The objective of this project is to investigate the stability of fixed points using stability analysis and phase portrait. After that, we compare the results of stability obtained from both approaches. Our observations indicate that results of stability using both approaches are same. This means that both approaches are suitable to explain the behavior of the solutions, especially when deal with real world problems. This research is important for the sustaining of interacting species of prey and predator populations in an ecosystem.