  We demonstrate neuron-like spiking dynamics in the asymmetrically driven
dissipative photonic Bose-Hubbard dimmer model which describes two coupled
nonlinear passive Kerr cavities. Spiking dynamics appear due to the excitable
nature of the system. In this context, excitable excursions in the phase space
correspond to spikes in the temporal evolution of the field variables. In our
case, excitability is mediated by the destruction of an oscillatory state in a
global homoclinic bifurcation. In this type of excitability (known as type-I)
the period of the oscillatory state diverges when approaching the bifurcation.
Beyond this point, the system exhibits excitable dynamics under the application
of suitable perturbations. We have also characterized the effect that additive
Gaussian noise has on the spiking dynamics, showing that the system undergoes a
coherence resonance for a given value of the noise strength.
