The route from linear towards nonlinear and chaotic aerodynamic regimes of a fixed dragonfly wing cross section in gliding flight is investigated numerically using direct Navier-Stokes simulations (DNSs). The dragonfly wing consists of two corrugations combined with a rear arc, which is known to provide overall good aerodynamic mean performance at low Reynolds numbers. First, the three regimes (linear, nonlinear, and chaotic) are characterized, and validated using two different fluid solvers. In particular, a peculiar transition to chaos when changing the angle of attack is observed for both solvers: The system undergoes a sudden transition to chaos in less than 0.1^{∘}. Second, a physical insight is given on the flow interaction between the corrugations and the rear arc, which is shown as the key phenomenon controlling the unsteady vortex dynamics and the sudden transition to chaos. Additionally, aerodynamic performances in the three regimes are given, showing that optimal performances are closely connected to the transition to chaos.