Accordingly the embodiments herein provide a method for fabricating a neuron oscillator (200a). The neuron oscillator (200a) includes a thermal insulating device connected with a resistor and a capacitor in series to produce self-sustained oscillations, where the resistor and the capacitor are arranged in parallel manner. The neuron oscillator (200a) eliminates a requirement of an additional compensation circuitry for a consistent performance over a time under heating issues. Additionally, an ON/OFF ratio of the neuron oscillator (200a) improves to a broader resistor range. Further, a presence of tunable synaptic memristor functionality of the neuron oscillator (200a) provides a reduced fabrication complexity to a large scale ONN. An input voltage required for the neuron oscillator (200a) is low (2-3 V) which makes it suitable to use with existing circuitries without using any additional converters. Additionally, an amplitude of the oscillations is a significant fraction of an applied bias which eliminates a need for an amplification.