  A novel analysis of homogeneous nucleation of dislocations in sheared
two-dimensional crystals described by periodized discrete elasticity models is
presented. When the crystal is sheared beyond a critical strain $F=F_{c}$, the
strained dislocation-free state becomes unstable via a subcritical pitchfork
bifurcation. Selecting a fixed final applied strain $F_{f}>F_{c}$, different
simultaneously stable stationary configurations containing two or four edge
dislocations may be reached by setting $F=F_{f}t/t_{r}$ during different time
intervals $t_{r}$. At a characteristic time after $t_{r}$, one or two dipoles
are nucleated, split, and the resulting two edge dislocations move in opposite
directions to the sample boundary. Numerical continuation shows how
configurations with different numbers of edge dislocation pairs emerge as
bifurcations from the dislocation-free state.
