Noise-induced transitions in random Pomeau–Manneville maps

We introduce randomness to Pomeau–Manneville (PM) maps by incorporating dichotomous multiplicative noise that alternates between dynamics with an attracting and a repelling fixed point. We characterize the dynamical behavior by measuring the separation of two nearby orbits. Controlling the probability of selecting the repelling PM map, we find two noise-induced transitions. When the repelling map is selected with probability less than 1/2, orbits converge to the origin, which is an indifferent fixed point shared by both maps. When the selection probability exceeds 1/2, nearby orbits contract. When the noise-averaged PM map exhibits weak chaos, this leads to weak synchronization, where the distance between orbits asymptotically approaches zero at a subexponential rate. Further increases in the selection probability lead to the second transition to chaotic or weakly chaotic behavior, depending on whether the noise-averaged PM map exhibits chaos or weak chaos, respectively. Additionally, we show that a power-law exponent of 3/2 in the sojourn-time distribution near the indifferent fixed point is universally observed at the first transition point. These results provide insights into how introducing multiplicative noise to chaotic or weakly chaotic systems can lead to rich dynamical behaviors, shedding light on the effects of noise in intermittent dynamical systems.