Asymptotic behavior of a difference equation model in exponential form

We investigate the global stability and the convergence rate of the exponential model: where . The initials , and and the parameters , and are non‐negative real numbers. We also discuss the unboundedness, persistence, and boundedness of this system. Moreover, we introduce conditions for uniqueness and existence of the equilibrium. Finally, we give numerical explanations to verify our results. We can use the above system as a model for the growth of some perennial plants and their relationships with each other.