Lyapunov Graph of Lozi System and Corresponding MATLAB Implementation

This article provides a comprehensive exploration of the Lyapunov graph for the Lozi system along with its corresponding MATLAB implementation. The Lozi system represents a nonlinear dynamical system exhibiting chaotic behavior, characterized by complex dynamics and intricate attractor structures that have garnered significant attention in dynamics and physics research. The Lyapunov graph serves as a powerful visualization technique in phase space, enabling researchers to better comprehend system behavior through graphical representation of dynamic evolution. Our discussion includes detailed MATLAB code implementation strategies for generating Lyapunov graphs of the Lozi system, covering essential algorithmic components such as system parameter initialization, iteration schemes for chaotic map calculation, and Lyapunov exponent computation methods. The implementation utilizes MATLAB's plotting capabilities for phase space visualization and incorporates numerical techniques for stability analysis. We further examine analytical approaches for interpreting the generated graphs, including bifurcation pattern identification and attractor characterization. The article also investigates fundamental properties and practical applications of the Lozi system in chaos theory, along with prospective research directions involving parameter sensitivity analysis and system control methodologies. The MATLAB code implementation demonstrates efficient computation of iterative maps using vectorized operations and includes visualization best practices for effective graphical representation of complex dynamical behavior.