New Algorithm for Detecting Malicious Links Through Chaotic Dynamics Analysis

\section*{Code Description}

This Jupyter notebook implements a \textbf{Link Safety Analyzer} based on chaos theory for detecting malicious or suspicious web links. 
It models the browsing process as a nonlinear dynamical system and quantifies instability through:

\begin{itemize}
  \item \textbf{Lyapunov Exponent ($\lambda$):} measures sensitivity to initial conditions by comparing two slightly perturbed browsing sessions.
  \item \textbf{Finite-Time Divergence Entropy ($H$):} captures unpredictability in execution traces as a proxy for Kolmogorov--Sinai entropy.
\end{itemize}

\subsection*{Main Features}
\begin{itemize}
  \item Uses \texttt{Selenium} with a headless Chrome browser to simulate visits to a given URL.
  \item Collects runtime telemetry at each step, including:
    \begin{itemize}
      \item CPU utilization
      \item Memory consumption
      \item DOM size (number of elements)
      \item Number of active scripts
    \end{itemize}
  \item Executes each URL twice with slight perturbations to generate divergence trajectories.
  \item Computes \textbf{Lyapunov exponent} and \textbf{entropy} from trajectory separation.
  \item Produces a unified visualization (divergence curve, computed metrics, and safety verdict).
  \item Classifies links into three categories: \textbf{SAFE, CAUTION, UNSAFE}.
\end{itemize}

\subsection*{Intended Use}
The notebook serves as a prototype research tool to demonstrate the effectiveness of chaos-theoretic indicators for cybersecurity. 
It is not a production-ready detector but a proof-of-concept that supports the results of the accompanying paper 
\emph{``Detecting Malicious Links Through Chaotic Dynamics Analysis''}.