  Two distinct transition points have been observed in a problem of lattice
percolation studied using a system of pulsating discs. Sites on a regular
lattice are occupied by circular discs whose radii vary sinusoidally within
$[0,R_0]$ starting from a random distribution of phase angles. A lattice bond
is said to be connected when its two end discs overlap with each other.
Depending on the difference of the phase angles of these discs a bond may be
termed as dead or live. While a dead bond can never be connected, a live bond
is connected at least once in a complete time period. Two different time scales
can be associated with such a system, leading to two transition points. Namely,
a percolation transition occurs at $R_{0c} =0.908$ when a spanning cluster of
connected bonds emerges in the system. Here, information propagates across the
system instantly, i.e., with infinite speed. Secondly, there exists another
transition point $R_0^* = 0.5907$ where the giant cluster of live bonds spans
the lattice. In this case the information takes finite time to propagate across
the system through the dynamical evolution of finite size clusters. This
passage time diverges as $R_0 \to R_0^*$ from above. Both the transitions
exhibit the critical behavior of ordinary percolation transition. The entire
scenario is robust with respect to the distribution of frequencies of the
individual discs. This study may be relevant in the context of wireless sensor
networks.
