We study the rheology of a soft particulate system where the inter-particle interactions are weakly attractive. Using extensive molecular dynamics simulations, we scan across a wide range of packing fractions ($phi$), attraction strengths ($u$) and imposed shear-rates ($dot{gamma}$). In striking contrast to repulsive systems, we find that at small shear-rates generically a fragile isostatic solid is formed even if we go to $phi ll phi_J$. Further, with increasing shear-rates, even at these low $phi$, non-monotonic flow curves occur which lead to the formation of persistent shear-bands in large enough systems. By tuning the damping parameter, we also show that inertia plays an important role in this process. Furthermore, we observe enhanced particle dynamics in the attraction-dominated regime as well as a pronounced anisotropy of velocity and diffusion constant, which we take as precursors to the formation of shear bands. At low enough $phi$, we also observe structural changes via the interplay of low shear-rates and attraction with the formation of micro-clusters and voids. Finally, we characterize the properties of the emergent shear bands and thereby, we find surprisingly small mobility of these bands, leading to prohibitely long time-scales and extensive history effects in ramping experiments.
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