  Using numerical simulations, the rheological response of an athermal assembly
of soft particles with tunable attractive interactions is studied in the
vicinity of jamming. At small attractions, a fragile solid develops and a
finite yield stress is measured. Moreover, the measured flow curves have
unstable regimes, which lead to persistent shearbanding. These features are
rationalized by establishing a link between the rheology and the inter-particle
connectivity, which also provides a minimal model to describe the flow curves.
