The development of compact and low-power solid state oscillators is of increasing interest for use as solid-state neurons in oscillatory neural networks (ONNs) for hardware based artificial intelligence and neuromorphic computing. Metal-oxide-metal (MOM) devices can exhibit volatile negative differential resistance (NDR) which provides a basis for fabricating such oscillators. Oscillation behaviour is governed by the NDR characteristics of the functional oxide layer and NDR comes from temperature-dependent conductivity of the oxide layer. The oxides which show insulator-to-metal transition (IMT) at a certain temperature are suitable for low power operation due to their large conductivity change over a narrow temperature range. Among the oxides which exhibit reliable NDR, VO2 and NbO2 are two of them but the IMT temperature of VO2 (TIMT~340 K) is below the typical operating temperature (400 K) of modern computers and NbO2 (TIMT~1070K) consumes large energy during switching. Hence, new materials for solid-state neurons that can operate at temperatures compatible with modern computing architectures are urgently needed to realise the promise of NDR based neuromorphic computing. As part of my PhD research I have been studying the volatile NDR characteristics of V3O5, which has the highest IMT temperature (TIMT=420 K) of the vanadium-oxide Magnéli (VnO2n-1) phases. The V3O5 MOM memristor devices show reliable volatile NDR characteristics with stable (<3% variation) cycle-to-cycle operation.  The physical mechanisms underpinning these characteristics are investigated using a combination of electrical measurements, in-situ thermal imaging and device modelling. This shows that the conduction in lateral MOM device structures is confined to a narrow filamentary path due to self-confinement of the current distribution, and that NDR response is initiated at temperatures well below the IMT temperature where it is dominated by the temperature dependence of the insulating phase.   Finally, I investigate the dynamics of individual and coupled V3O5-based relaxation oscillators, and show that capacitively coupled devices exhibit rich non-linear dynamics, including frequency and phase synchronisation. These results establish V3O5 as a new functional material for volatile threshold switching to advance the development of robust solid-state neurons for neuromorphic computing.