The collective behavior of many coupled oscillator systems is currently being explored for the implementation of different non-conventional computing paradigms. In particular, VO2 based nano-oscillators have been proposed to implement oscillatory neural networks that can serve as associative memories, useful in pattern recognition applications. Although the dynamics of a pair of coupled oscillators have already been extensively analyzed, in this brief, the topic is addressed more practically. Firstly, for the application mentioned above, each oscillator needs to be initialized in a given phase to represent the input pattern. We demonstrate the impact of this initialization mechanism on the final phase relationship of the oscillators. Secondly, such oscillatory networks are based on frequency synchronization, in which the impact of variability is critical. We carried out a comprehensive mathematical analysis of a pair of coupled oscillators taking into account both issues, which is a first step towards the design of the oscillatory neural networks for associative memory applications.