Collected Bifurcation Diagrams of the Lorenz System

In this document, I present my curated collection of bifurcation diagrams for the Lorenz system. These diagrams were generated through rigorous research and analysis, featuring multiple representations that demonstrate various computational methods and techniques. Implementation typically involves numerical integration algorithms (e.g., Runge-Kutta methods) with systematic parameter variation, particularly adjusting the Rayleigh parameter while tracking system stability transitions. The diagrams reveal fascinating patterns and regularities in the system's behavior, including period-doubling routes to chaos and crisis events. These observed patterns provide valuable insights for deeper investigation and analysis of nonlinear dynamics. Importantly, the collection serves as a significant reference for further exploration of the Lorenz system, offering concrete examples of how bifurcation analysis can be implemented programmatically using phase-space reconstruction and Poincaré section techniques.