  Using high-resolution 3-D and 2-D (axisymmetric) hydrodynamic simulations in
spherical geometry, we study the evolution of cool cluster cores heated by
feedback-driven bipolar active galactic nuclei (AGN) jets. Condensation of cold
gas, and the consequent enhanced accretion, is required for AGN feedback to
balance radiative cooling with reasonable efficiencies, and to match the
observed cool core properties. A feedback efficiency (mechanical luminosity
$\approx \epsilon \dot{M}_{\rm acc} c^2$; where $\dot{M}_{\rm acc}$ is the mass
accretion rate at 1 kpc) as small as $5 \times 10^{-5}$ is sufficient to reduce
the cooling/accretion rate by $\sim 10$ compared to a pure cooling flow. This
value is smaller compared to the ones considered earlier, and is consistent
with the jet efficiency and the fact that only a small fraction of gas at 1 kpc
is accreted on to the supermassive black hole (SMBH). We find hysteresis cycles
in all our simulations with cold mode feedback: {\em condensation} of cold gas
when the ratio of the cooling-time to the free-fall time ($t_{\rm cool}/t_{\rm
ff}$) is $\lesssim 10$ leads to a sudden enhancement in the accretion rate; a
large accretion rate causes strong jets and {\em overheating} of the hot ICM
such that $t_{\rm cool}/t_{\rm ff} > 10$; further condensation of cold gas is
suppressed and the accretion rate falls, leading to slow cooling of the core
and condensation of cold gas, restarting the cycle. Therefore, there is a
spread in core properties, such as the jet power, accretion rate, for the same
value of core entropy or $t_{\rm cool}/t_{\rm ff}$. A fewer number of cycles
are observed for higher efficiencies and for lower mass halos because the core
is overheated to a longer cooling time. The 3-D simulations show the formation
of a few-kpc scale, rotationally-supported, massive ($\sim 10^{11} M_\odot$)
cold gas torus. (abstract abridged)
