The present thesis investigates circuit‑level strategies for coupling electrical oscillators based on the phase‑change material vanadium dioxide (VO₂). The growing interest in brain‑inspired computing paradigms has brought resistive switching devices to the forefront, as they combine in‑memory processing capabilities with back‑end‑of‑line (BEOL) compatibility, making them promising alternatives to conventional CMOS technologies. When interconnected, VO₂ relaxation oscillators exchange electrical energy and naturally evolve toward phase synchronization, forming stable dynamical states characterized by fixed phase relationships. Such synchronized oscillator networks can emulate an Oscillatory Neural Network (ONN), a class of Artificial Neural Network capable of solving simple combinatorial optimization problems. The thesis first introduces the broader context of neuromorphic computing, and ONNs, emphasizing the advantages of VO₂‑based oscillators for hardware‑efficient computation.