  Systems with the coexistence of different stable attractors are widely
exploited in systems biology in order to suitably model the differentiating
processes arising in living cells. In order to describe genetic regulatory
networks several deterministic models based on systems of nonlinear ordinary
differential equations have been proposed. Few studies have been developed to
characterize how either an external input or the coupling can drive systems
with different coexisting states. For the sake of simplicity, in this
manuscript we focus on systems belonging to the class of radial isochron clocks
that exhibits hard excitation, in order to investigate their complex dynamics,
local and global bifurcations arising in presence of constant external inputs.
In particular the occurrence of saddle node on limit cycle bifurcations is
detected.
