<p>We propose the analysis and dynamical system model for one-dimensional bistable Physically Unclonable Function (PUF). Our work is derived from the analysis of a broad range of analytical models and circuit topologies suitable for the design of bistable PUFs. Starting from circuit analysis, we discuss a theoretical model to evaluate the source of entropy from a mathematical point of view targeting optimized intrinsic hardware-based security mechanisms. The results develop an evaluation design tool to address the most crucial model parameters affecting the obtained system uniqueness. The analysis is authentic as it is generalized by a systematic standpoint framing the PUF design within a mathematical context. The paper presents a methodical approach aiming at defining a novel class of beneficial models exploiting the dynamics sensitivity to parametric perturbations extending the PUF design within a theoretical setting. Furthermore, the proposed analysis is potentially investigated to explore the impacts of environmental conditions on system parametric perturbation affecting PUF reliability.</p>