Yogyakarta which is a small town in Indonesia gets a terrible jamming. This paper purposes to analyze the condition of traffic by looking at the local stability of the Lorentz system. The stability analysis is performed using Routh-Hurwitz criterion at hyperbolic equilibrium point, while at non-hyperbolic equilibrium point isused the center manifold. The result shows that whenever the traffic condition is crowded but smooth, congestion will be possible when the initial condition is in the  neighborhood. Equilibrium  is an unstable equilibrium. Equilibrium  is a stable equilibrium. If traffic conditions are in the  neighborhood, there will be no congestion. Numerical simulations show that vehicle mileage with initial values around  is at approximately the optimal distance. This can be used as a reference in managing traffic light systems.

traffic jamming, Lorentz system, local stability, Routh-Hurwitz criterion, center manifold.