Summary
Optical systems that feature some sort of coupling between various subsystems offer a flexible platform to observe a diverse range of rich nonlinear dynamics. Often, the vector fields that describe the dynamics of such coupled systems have within them a natural symmetry that can lead to either delocalization or symmetry breaking. We consider a microresonator that supports two interacting electric fields, generated by two laser beams of equal properties. Mathematically, this system is modeled by a four-dimensional $\mathbb{Z}_2$-equivariant vector field with strength and detuning of the input light as parameters. We identify a symmetric pair of heteroclinic cycles as an organizing center in the parameter plane. Different types of dynamics nearby are determined by means of the identification and continuation of global bifurcations in combination with the computation of kneading invariants and Lyapunov exponents. In this way, we provide a numerical unfolding of this codimension-two global bifurcation and show how it involves infinitely many further global bifurcations.
