Self-pulsing and chaos in the asymmetrically driven dissipative photonic Bose-Hubbard dimer: A bifurcation analysis.

We perform a systematic study of the temporal dynamics emerging in the asymmetrically driven dissipative Bose-Hubbard dimer model. This model successfully describes the nonlinear dynamics of photonic diatomic molecules in linearly coupled Kerr resonators coherently excited by a single laser beam. Such temporal dynamics may include self-pulsing oscillations, period doubled oscillatory states, chaotic dynamics, and spikes. We have thoroughly characterized such dynamical states, their origin, and their regions of stability by applying bifurcation analysis and dynamical system theory. This approach has allowed us to identify and classify the instabilities, which are responsible for the appearance of different types of temporal dynamics.