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In this paper, we consider coupled quantum-dot cells, which are usually used for quantum-dot cellular automata, to build nanoscale dynamical systems. In particular, it is shown how the simple connection of few quantum-dot cells, quantum cellular nonlinear networks (Q-CNNs), can cause the onset of chaotic oscillations. Complex dynamics can be obtained only with small differences of polarizations and parameters. Local activity conditions are investigated for a two-cells case satisfying the criteria for the generation of complex spatio-temporal behaviors. The richness of dynamics of quantum CNNs is also emphasized through examples of synchronization in an array of so-built oscillators, in both cases of identical parameters and spatial dissymmetry.