Stability analysis of a discrete type population model

This thesis consists of 4 sections. In the first chapter, the literature review on the thesis topic is presented and the basic definitions and theorems that will be used in the thesis study are given. In the second chapter, a continuous-time population model is derived by adding a refuge effect and an intra-species competition parameter for the predator population to the existing Lotka-Volterra type model in the literature. Then, the model is converted to discrete time by using the non-standard discretization method. Finally, the equilibrium points of this discrete-time system are determined, and stability analyses are conducted. The third chapter, titled "Numerical Studies," involves numerical simulations that support the theoretical findings. These simulations visually demonstrate how the refuge effect and intra-species competition in the predator population influence population dynamics under different scenarios. The fourth chapter consists of the "Discussion, Conclusion and Suggestions" section, where the data obtained from these studies conducted in the thesis are presented.