When b=0, this system is conservative and produces quasi-periodic motions as evidenced in the Poincaré section defined by y=0 and shown in Fig. 1. Using x0 = 0.1417, y0=z0=0, there is most likely a weakly chaotic toroidal motion (shown in green in Fig. 1.).
 O. E. Rössler, C. Kahlert & B. Uehleke, Tori and chaos in a simple C1-system, Lectures Notes in Engineering, 13, 51-58, 1985.