  In this paper a stability analysis for a Cournot duopoly model with tax
evasion and time-delay in a continuous-time framework is presented. The
mathematical model under consideration follows a gradient dynamics approach, is
nonlinear and four-dimensional with state variables given by the production and
declared revenue of each competitor. We prove that both the marginal cost rate
and time delay play roles as bifurcation parameters. More precisely, if the
marginal cost rate lies in certain closed interval then the equilibrium point
is delay-independent stable, otherwise it is delay-dependent stable and a Hopf
bifurcation necessarily occurs. Some numerical simulations are presented in
order to confirm the proposed theoretical results and illustrate the effect of
the bifurcation parameters on model stability.
