Oscillator networks with N-shaped nonlinearities: Electrical modeling and wave digital emulation

This paper proposes contributions to the efficient wave digital (WD) modeling of large oscillator networks which are emerging as energy-efficient alternatives to traditional computers. The WD concept enables in-operando parameter tuning, real-time testing, and the associated algorithms are highly parallelizable. We present a general electrical model of N-shaped nonlinearities that are commonly found in nonlinear oscillators. Our model offers the flexibility to design the current–voltage characteristic based on specific requirements. We show how this model can be used to derive efficient and explicit WD algorithms for nonlinear oscillators. Furthermore, we propose the use of lossless transmission lines between the oscillators and the coupling network to obtain an ideal circuit for an oscillator network that can function as an Ising machine and be efficiently and exactly evaluated in the WD domain. The proposed algorithms are compared against the classical method involving iterative techniques, and their capabilities are evaluated through the emulation of a single FitzHugh-Nagumo oscillator as well as an Ising machine involving transmission lines. In the latter case, we show that, for large networks, the proposed methods decrease the runtime by up to 75% compared to using iterative techniques.