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

Abstract

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 include self-pulsing oscillations, period doubled oscillatory states, chaotic dynamics, and spikes. The different states and dynamical regimes have been thoroughly characterized using bifurcation analysis. This analysis has allowed us to identify the main instabilities, i.e. bifurcations, responsible for the appearance of the previously stated dynamics.

Neuron-like spiking dynamics in the asymmetrically-driven dissipative photonic Bose-Hubbard dimer

“…In a previous work, we have analyzed the temporal dynamics arising in this system [35,36]. Applying bifurca- tion analysis and path-continuation techniques [37,38], through the free software package AUTO-07p [39], we were able to classify the region of existence of the different dynamical regimes such as self-pulsing oscillations and chaos [36]. This analysis predicted that for a coupling constant value C ≈ 1 the continuous-wave state becomes unstable for ∆ 1 2.1, leading to stable permanent oscillations.…”

“…From the right of the resonance, periodic oscillations also emerge from H b , but soon after that, they die at Hom. This homoclinic bifurcation involves the collision of a limit cycle and a saddle-node type equilibrium and is known as tame Shilnikov homoclinic bifurcation [36,40]. These kind of bifurcations are characterized by the exponential divergence of the cycles period T when approaching Hom.…”