  We first construct a dynamical systems model which in its steady-state serves
as an analytic continuation of the completed Riemann zeta function over the
entire critical strip. The resulting mathematical construct involves a linear
interpolation of two symmetric generator functions which can be used to infer
the global properties of the non-trivial zeros of the Riemann zeta function
using concentration bounds. The proposed dynamical systems framework thus
provides an alternative method for investigating the celebrated Riemann
Hypothesis which is shown in this paper to be almost surely true. We also show
that the framework is general enough to study the non-trivial zeros of the
Dirichlet L-functions and in this paper we show that under specific conditions,
the generalized Riemann Hypothesis is also almost surely true.
