Solving Variable-Parameter Lorenz Equations Using MATLAB

In nonlinear dynamics and chaos research, MATLAB is frequently employed to solve variable-parameter Lorenz equations and similar problems. This program utilizes MATLAB's ODE solvers (such as ode45 or ode15s) with customizable parameter inputs to handle differential equation systems with varying parameters. The implementation allows users to modify system parameters dynamically through function arguments or external configuration files. Beyond Lorenz equations, the program can solve other variable-parameter systems including Chen system, Lü system, and Rössler system by adapting the governing equations in the differential function file. These systems find broad applications in meteorology, biology, communications, and other fields. Key implementation aspects include: defining derivative functions with parameter arguments, implementing adaptive step-size control for numerical stability, and visualizing results using phase portraits and time-series plots. Mastering these solution techniques is crucial for researchers and engineers working in related domains, particularly for studying bifurcation behavior and chaotic phenomena under parameter variations.