Exploring Non-linear Dynamics: Constructing the Bifurcation Diagram of a Damped Driven Pendulum Using Python

A detailed analysis and construction of the bifurcation diagram for a damped driven pendulum using Python. The damped driven pendulum, a classic example of a non-linear dynamic system, exhibits complex behaviors that are highly sensitive to initial conditions and system parameters. By employing numerical methods and leveraging Python’s scientific libraries, we systematically explore the system's response over a range of drive strength. The bifurcation diagram, which maps the qualitative changes in the pendulum’s steady-state behavior as a function of these parameters, reveals intricate patterns of periodicity, quasi-periodicity, and chaotic regimes. Our findings highlight the critical thresholds where the system transitions from regular to chaotic motion, providing insights into the underlying mechanisms driving these dynamics.