  We investigate the nonlinear optical response of suspended 1D photonic
crystal nanocavities fabricated on a silicon nitride chip. Strong
thermo-optical nonlinearities are demonstrated for input powers as low as
$2\,\mu\text{W}$ and a self-sustained pulsing regime is shown to emerge with
periodicity of several seconds. As the input power and laser wavelength are
varied the temporal patterns change in period, duty cycle and shape. This
dynamics is attributed to the multiple timescale competition between
thermo-optical and thermo-optomechanical effects and closely resembles the
relaxation oscillations states found in mathematical models of neuronal
activity. We introduce a simplified model that reproduces all the experimental
observations and allows us to explain them in terms of the properties of a 1D
critical manifold which governs the slow evolution of the system.
