  We investigate two homogeneous networks: the Watts-Strogatz network and the
random Erdos-Renyi network, the latter with tunable clustering coefficient $C$.
The network is an area of two competing contact processes, where nodes can be
in two states, S or D. A node S becomes D with probability 1 if at least two
its mutually linked neighbours are D. A node D becomes S with a given
probability $p$ if at least one of its neighbours is S. The competition between
the processes is described by a phase diagram, where the critical probability
$p_c$ depends on the clustering coefficient $C$. For $p>p_c$ the rate of state
S increases in time, seemingly to dominate in the whole system. Below $p_c$,
the contribution of D-nodes remains finite. The numerical results, supported by
mean field approach, indicate that the transition is discontinuous.
