Bifurcation Diagram Computation Program for 2D Discrete Systems

This program enables the computation of bifurcation diagrams for two-dimensional discrete systems, commonly utilized in nonlinear dynamics and complex economic modeling. The implementation employs iterative parameter sweeping with nested loops to track system evolution, storing trajectory data for visualization. Through appropriate modifications to the state transition functions, this code can be extended to plot bifurcation diagrams for higher-dimensional discrete mapping systems. The program provides practical assistance in understanding and analyzing dynamic system behaviors, facilitating exploration of various nonlinear system characteristics. Key algorithmic components include state initialization, transient removal, and Lyapunov exponent calculation for stability assessment. The bifurcation diagram generation uses MATLAB's scatter plotting capabilities to display period-doubling routes to chaos and other dynamic phenomena. This versatile tool finds applications across multiple disciplines including physics, chemistry, biology, and engineering sciences, offering solutions for investigating complex real-world problems involving nonlinear discrete systems. The modular code structure allows easy adaptation to specific system equations and parameter ranges.