Simulation of a Chaotic System

This documentation presents a MATLAB implementation for simulating chaotic systems. The core computational framework is built around lyapunov.m, which serves as the main driver program. We provide qi_hyper.m as a demonstrative example implementing the Qi system. The qi_hyper_lyap.m function calculates all Lyapunov exponents using numerical integration techniques, while qi_hyper_lyapDim.m computes the fractal dimension through dimension estimation algorithms. The program architecture allows easy adaptation to other chaotic systems through parameter modifications and system equation updates. Our implementation employs advanced numerical methods including Runge-Kutta integration and Gram-Schmidt orthogonalization for stable exponent calculation. Validation tests confirm our solution demonstrates superior efficiency and accuracy compared to alternative Lyapunov exponent computation methods. These MATLAB tools provide researchers with a robust foundation for chaotic system simulation studies.