We conduct a theoretical study of the nonlinear optical response of a two-dimensional semiconductor quantum dot supercrystal subjected to a quasi-resonant continuous wave excitation. A constituent quantum dot is modeled as a three-level ladder-like system (comprising the ground, the one-exciton, and the bi-exction states). To study the stationary response of the supercrystal, we propose an exact linear parametric method of solving the nonlinear steady-state problem, while to address the supercrystal optical dynamics qualitatively, we put forward a novel method to calculate the bifurcation diagram of the system. Analyzing the dynamics, we demonstrate that the supercrystal can exhibit multistability, periodic and aperiodic self-oscillations, and chaotic behavior, depending on parameters of the supercrystal and excitation conditions. The effects originate from the interplay of the intrinsic nonlinearity of quantum dots and the retarded inter-dot dipole-dipole interaction. The latter provides a positive feedback which results in the exotic supercrystal optical dynamics. These peculiarities of the supercrystal optical response open up a possibility for all-optical applications and devices. In particular, an all-optical switch, a tunable generator of THz pulses (in self-oscillating regime), a noise generator (in chaotic regime), and a tunable bistable mirror can be designed. a b c FIG. 1. PbSe rocksalt 2D nanostructures with (a) honeycomb and (b) square lattice symmetry, (c) -CdSe nanostructure with a compressed zincblende and slightly distorted square lattices (scale bars, 50 nm). Insets show the electrodiffractograms in the [111] (a) and [100] (b,c) projections. The figure is from Ref. [7].linearity of the layer is ensured by the fact that two-level emitters are nonlinear systems. The positive feedback originates from the secondary field, which is generated by the emitters themselves; this is the so-called intrinsic feedback, i.e., here a cavity (external feedback) is not required.A two-dimensional (2D) semiconductor quantum dot (SQD) supercrystal represents a limiting case of a thin layer. In this paper, we conduct a theoretical study of the nonlinear optical response of such a system. A single SQD is considered as a point-like system with three consecutive levels of the ground, one-exciton, and bi-arXiv:1910.02553v1 [physics.optics]