Computation of Bifurcation Points in 3-Dimensional Systems

To generate a bifurcation diagram for a 3-dimensional dynamical system using MATLAB, you can implement a numerical continuation approach. First, define the system's governing equations using function handles or symbolic math tools, ensuring proper parameterization. Then employ MATLAB's built-in ODE solvers (e.g., ode45) combined with root-finding algorithms (e.g., fzero) to detect bifurcation points where system stability changes. Key implementation steps include setting up parameter sweeps, tracking equilibrium points using predictor-corrector methods, and applying Floquet multipliers for stability assessment. The resulting visualization will display bifurcation branches (saddle-node, Hopf, pitchfork) using different line styles and colors, with customizable axes labels and color mapping to distinguish stable/unstable solutions. For enhanced clarity, incorporate interactive plot features using MATLAB's graphics objects to highlight critical parameter values where bifurcations occur.