  In this paper, we analyze the stability, convergence, and bifurcation
properties of the Boissonade-De Kepper (BD) model which played a key role in
the development of nonlinear chemical dynamics. We first outline conditions for
local stability, which may help guide design considerations. Then, we show that
the BD model undergoes a Hopf bifurcation when the stability condition gets
violated. Using Poincar\'{e} normal forms and center manifold theory, we derive
explicit analytic expressions for determining the type of the Hopf bifurcation
and the stability of the limit cycles. This provides insights on the system
dynamics just beyond the stable regime. Some of the analytical insights are
corroborated with numerical computations. We also show that the mathematical
results obtained in this paper may have wider applicability beyond the BD
model.
