Compatibility of local and global stability conditions for some discrete population models

In this paper, we investigate the stability of the model that has been proposed to study the growth of Bobwhite Quail Populations of Northern Wisconsin and prove that local stability implies global stability. We will prove the main results by using a suitable Lyapunov function and for illustration we apply the results on Hassell and Smith models. Also, we will show that for different values of the parameters, the population will exhibit variations in dynamics. Some illustrative examples and graphs are included to demonstrate the validity and applicability of the results.