Using a network modelling approach to model adaptive dynamical systems based on self-modeling networks, this paper present a computational analysis of password-based authentication systems. It reveals several key insights into the interplay between user experience (UX) and security. An important finding is the tension between security and usability in password systems. While these systems are ubiquitous due to their relative ease of implementation and user familiarity, they come with significant challenges. As for users often convenience is more important than security, they use weak, easily guessable passwords and password reuse across multiple accounts. This behaviour, also driven by the cognitive burden of managing numerous passwords, has a bad impact on the risk of unauthorized access and security breaches. Computational analysis also showed that with adequate training, the usability of 2FA systems improved, leading to a reduction in user stress over time.