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Rare events in mixed-mode oscillations from weakly coupled lasers.

We study a dynamical system consisting of two mutually coupled molecular lasers, each of which shows mixed-mode oscillations and chaos when uncoupled. The type of coupling, incoherent laser interaction via saturable absorbers is an example of inhibitory nonlinear coupling, which is also found in Hodgkin-Huxley models that describe action potentials in neurons. We have carried out extensive numerical bifurcation analysis and numerical simulations to show that for small-enough coupling, well below the chaotic synchronization threshold, the presence of distinctive resonances in a symmetric mirror configuration of the system generates a type of rare events characterized by very small amplitudes. When this symmetry is broken by introducing a relatively small difference between the lasers pump parameters near an in-phase Hopf bifurcation, we observe extreme rare events (rogue waves) in one of the lasers. In this case the outliers deviate from power-law distributions and are reminiscent of those known as dragon kings. We consider the conditions for both types of rare events to occur, their origin, as well as relevant statistical features.