In this article, we investigate the dynamics of traffic flows and their relationship with phase transitions using the complex Lorenz model. The research focuses on the impact of frequency detuning ( \(\Delta \) ) on the stability of solutions and the emergence of double periodicity in the model. Using analytical methods and numerical experiments, we analyze the stability of equilibrium states and the influence of frequency detuning on bifurcations. Our results demonstrate that the system exhibits a double-periodic regime associated with symmetry breaking. This behavior can be interpreted as the emergence of traffic congestion. We also identify a critical detuning value ( \(\Delta _c\) ) at which the traffic flow stabilizes. These results provide insights into the mechanisms of traffic congestion and can contribute to the development and refinement of mathematical traffic flow models.
