  We consider certain types of discretization schemes for differential
equations with quadratic nonlinearities, which were introduced by Kahan, and
considered in a broader setting by Mickens. These methods have the property
that they preserve important structural features of the original systems, such
as the behaviour of solutions near to fixed points, and also, where appropriate
(e.g. for certain mechanical systems), the property of being volume-preserving,
or preserving a symplectic/Poisson structure. Here we focus on the application
of Kahan's method to models of biological systems, in particular to reaction
kinetics governed by the Law of Mass Action, and present a general approach to
birational discretization, which is applied to population dynamics of
Lotka-Volterra type.
