Bouncing cosmologies in the presence of a Dirac-Born-Infeld field

We perform a detailed dynamical system analysis for the behavior of a Dirac-Born-Infeld (DBI) field in a spatially closed Friedmann-Lema\^{}tre-Robertson-Walker (FLRW) cosmology. The DBI field is characterized by a potential and brane tension. We study power-law or exponential functions for the potential and tension. We find that in a spatially closed FLRW cosmology, a DBI field in the ultrarelativistic limit allows for a broader range of initial conditions resulting in a bouncing universe than in the nonrelativistic limit. We further note that the range of initial conditions allowing for a bounce is larger if we consider power-law functions for the potential and tension, compared to the exponential case. Our dynamical analysis shows that a DBI field does not exhibit stable cyclical behavior, including the case in which a negative cosmological constant is present.