Computing Lyapunov Exponent for Logistic Map
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This MATLAB program is designed to compute the Lyapunov exponent for the logistic map. The implementation utilizes numerical differentiation to analyze the exponential divergence rate of nearby trajectories in this nonlinear dynamical system. Key algorithmic components include iterative map evaluation using the logistic equation xₙ₊₁ = rxₙ(1-xₙ) and derivative accumulation through chain rule application. The program features parameter configuration for bifurcation parameter r and initial conditions, with built-in error handling for numerical stability. This tool enables quantitative chaos analysis in complex systems like financial markets and ecological modeling by measuring sensitivity to initial conditions. Users should verify parameter ranges (typically r ∈ [0,4]) and iteration counts to ensure convergence. The modular code structure permits extensions for other one-dimensional maps by modifying the evolution function and Jacobian calculation.
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