Global dynamics of generalized second-order Beverton–Holt equations of linear and quadratic type

Abstract

We inVestigate second-order generaliZed BeVerton–Holt difference equations of the form xn+1 = af(xn, xn−1), n = 0, 1, …, 1 + f(xn, xn−1) Where f is a function nondecreasing in both arguments, the parameter a is a positiVe constant, and the initial conditions x−1 and x0 are arbitrary nonnegatiVe numbers in the domain of f. We Will discuss seVeral interesting eXamples of such equations and present some general theory. In particular, We Will inVestigate the local and global dynamics in the eVent f is a certain type of linear or quadratic polynomial, and We eXplore the eXistence problem of period-tWo solutions