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.

本文提出了在连续时间框架下具有逃税和时滞的古诺双寡头模型的稳定性分析。所考虑的数学模型采用梯度动力学方法，是非线性的并且是四维的，状态变量由每个竞争对手的生产和声明的收入给出。我们证明边际成本率和时间延迟都充当分叉参数。更确切地说，如果边际成本率处于某个封闭区间内，则平衡点是与延迟无关的稳定的，否则，它是与延迟有关的稳定的，因此必然发生Hopf分支。为了证实理论结果并说明分叉参数对模型稳定性的影响，提出了一些数值模拟。