Resistive Coupling of Bistable Resistor-Based Oscillators for Oscillatory Neural Network

An oscillatory neural network (ONN) is demonstrated by coupling a set of bistable resistor-based oscillators (birillators) through a coupling resistor (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${R}_{\text {C}}$ </tex-math></inline-formula>). Each birillator is composed of a nonlinear bistable resistor (biristor) and a load resistor (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${R}_{\text {L}}$ </tex-math></inline-formula>), which are connected in series. The synchronization behavior of oscillations among the resistively coupled birillators varies according to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${R}_{\text {C}}$ </tex-math></inline-formula>. When an external sine-wave signal was applied to the resistively coupled birillators, the phase of the oscillations was binarized by second-harmonic injection locking (SHIL). These coupled birillators with SHIL solved combinatorial optimization problems.