Computing with complex-valued networks of phase oscillators

A computational paradigm based on phase-locked states of oscillators embedded in a complex-valued weighted network is introduced, and its efficiency and scalability in performing single-and multiple-input Boolean and non-Boolean operations are demonstrated. The paradigm introduces phase rotation mechanisms in each link of the network, without the need for external control loops, or adaptive mechanisms. We show that the proposed computation allows outperforming standard implementations of Boolean logic, by reducing the computational cost of operations, and permitting the construction of memory elements with single dynamical units.