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Systems with the coexistence of different stable attractors are widelyexploited in systems biology in order to suitably model the differentiatingprocesses arising in living cells. In order to describe genetic regulatorynetworks several deterministic models based on systems of nonlinear ordinarydifferential equations have been proposed. Few studies have been developed tocharacterize how either an external input or the coupling can drive systemswith different coexisting states. For the sake of simplicity, in thismanuscript we focus on systems belonging to the class of radial isochron clocksthat 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 isdetected.

Complex dynamics in hard oscillators: the influence of constant inputs