Critical mass and competing effect in chemotaxis: insights from an attraction–repulsion model with rotational fluxes

Abstract This paper studies the critical mass phenomenon in an attraction–repulsion chemotaxis system with rotation under zero-flux boundary conditions in a two-dimensional bounded domain with a smooth boundary. On one side, when attraction dominates repulsion (in a certain sense characterized by the system parameters), a threshold value of the total cellular mass is identified, which controls the finite-time blow-up or global boundedness of classical solutions. On the other side, when repulsion dominates or balances attraction, global boundedness of classical solutions is established for arbitrary initial data under radial symmetry and synchronized rotations. These are the first rigorous mathematical results concerning the critical mass phenomenon in an attraction–repulsion chemotaxis system with rotation.