  We study the response of an optical system with the Kerr nonlinearity
demonstrating Bloch oscillations to a periodic train of coherent pulses. It has
been found out that the intensity of the field excited in the system by pulses
resonantly depends on the train period. It is demonstrated numerically and
analytically that the response of the system is stronger when the period of the
driving pulses is commensurate with the period of the Bloch oscillations.
Moreover, large enough pulses are capable to induce the instabilities which
eventually lead to onset of chaotic Bloch oscillations of the wave-function
envelope bouncing both in time and space. The analysis reveals that these
instabilities are associated with period-doubling bifurcations. A cascade of
such bifurcations with increase of the pulses amplitude triggers the chaotic
behaviour.
