Discrete-time analogues of predator-prey models with monotonic or nonmonotonic functional responses

Discrete-time analogues of predator-prey models with monotonic and nonmonotonic functional responses are introduced, respectively. The discrete-time analogues are considered to be numerical discretizations of the continuous-time models and we study their dynamical characteristics. It is shown that the discrete-time analogues preserve the periodicity of the continuous-time models with monotonic functional responses. Moreover, it is the first time that multiplicity of periodic solutions are studied when modeled with nonmonotonic functional responses. Unlike other types of functional responses, nonmonotone functional response declines at high prey densities. Thus the existing arguments for obtaining bounds of solutions to the operator equation Lx = lambda Nx are inapplicable to our case and some new arguments are employed for the first time. (c) 2006 Elsevier Ltd. All rights reserved.