Stability analysis of the WASP-148 planetary system, assuming coplanar orbits. For fixed initial conditions, the phase space of the system is explored by varying the semimajor axis a_c and eccentricity e_c of the outer planet WASP-148c. The step size is 10⁻² in eccentricity and 10⁻³ in semimajor axis. For each initial conditions, the system is integrated over 50 kyr, and a stability criterion is derived with the frequency analysis of the mean longitude. The chaotic diffusion is measured by the variation in the frequencies. The color scale corresponds to values between − 9 (black) and − 3 (red) for the decimal logarithm of the stability index D used in Correia et al. (2010). The red zone corresponds to highly unstable orbits, while the dark blue region can be assumed to be stable on a billion-year timescale. The reduced-χ² level curves of the Newtonian fit are also plotted.