Self-oscillating filtration membranes having a lifelike pulsatile flow are prepared thanks to a synchronized coupling between a chemical oscillator and a responsive membrane. Commercial alumina membranes are superficially functionalized with pH-responsive poly(methacrylic acid) (PMAA) chains synthesized by reversible addition–fragmentation chain transfer (RAFT) polymerization of MAA in the presence of a catechol-based RAFT agent. The grafting of PMAA onto alumina, mediated through catechol chemisorption, is analyzed by X-ray photoelectron spectroscopy, scanning electron microscopy combined with energy-dispersive X-ray spectroscopy, and static water contact angle. Bromate–sulfite–ferrocyanide (BSF) is used as a chemical oscillator, enabling autonomous cyclic pH modulation between 3.5 and 6.5. The pH oscillations are setup in the conditions of membrane filtration inside a filtration cell thanks to a careful study of the bifurcation diagram showing the required conditions to reach the oscillation domain. Since PMAA has a pKa around 5.8, a periodic extension–contraction of the polymer chains is obtained during membrane filtration, which leads to a synchronized change in the membrane pore size. Chemically powered autonomous pulsatile flow with an impressive permeability cycles is observed with an effective chemomechanical feedback action of the membrane pore size change on the chemical oscillator mechanism.