Global stability of generalised Beddington model

What is it about?

This work is related to dynamics of a discrete-time density-dependent generalized Beddington model. Moreover, we investigate the existence and uniqueness of positive equilibrium point, boundedness character, local and global behavior of unique positive equilibrium point and the rate of convergence of positive solutions that converge to the unique positive equilibrium point of this model. Numerical examples are provided to illustrate theoretical discussion.

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Why is it important?

Global stability of discrete-time models is not an easy task. The main finding in this article is the investigation of parametric conditions under which the positive steady-state is globally asymptotically stable.