Discrete time population dynamics of a two-stage species with recruitment and capture

This work models and analyzes the dynamics of a two-stage species with recruitment and capture factors. It arises from the discretization of a previous model developed by Ladino and Valverde (2013), which represents a progress in the knowledge of the dynamics of ex- ploited populations. Although the methods used here are related to the study of discrete- time systems and are different from those related to continuous version, the results are similar in both the discrete and the continuous case what confirm the skill in the se- lection of the factors to design the model. Unlike for the continuous-time case, for the discrete-time one some (non-negative) parametric constraints are derived from the bio- logical significance of the model and become fundamental for the proofs of such results. Finally, numerical simulations show different scenarios of dynamics related to the analyti- cal results which confirm the validity of the model.