  We study (non-)integrability and the presence of chaos in gravity dual
backgrounds of strongly coupled gauge theories with unquenched flavor,
specifically of the four-dimensional N=2 super Yang-Mills theory and the
three-dimensional ABJM theory. By examining string motion on the geometries
corresponding to backreacted D3/D7 and D2/D6 systems, we show that integrable
theories with quenched flavor become non-integrable when the virtual quark
loops are taken into account. For the string solutions in the backreacted D3/D7
system, we compute the leading Lyapunov exponent which turns out to saturate to
a positive value as the number of flavors increases. The exponent depends very
weakly on the number of flavors when they approach the number of colors. This
suggests that once a particular flavor number in the theory is reached, a
further increase does not lead to more severe chaotic phenomena, implying
certain saturation effects on chaos.
