MATLAB Implementation of Poincare Section for Autonomous Systems
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The objective of this project is to implement the Poincare section for autonomous systems using MATLAB programming. Achieving this goal requires utilizing ordinary differential equation (ODE) solvers to compute the Poincare section equations, along with MATLAB's plotting capabilities to visualize results and analyze system stability. The implementation involves using MATLAB's ode45 function - an adaptive Runge-Kutta method for solving non-stiff differential equations - to numerically integrate the system dynamics. Following the ODE solution, the project employs MATLAB's plot function to graphically represent the Poincare section, which captures system behavior at specific cross-sections of phase space. The implementation requires careful parameter tuning and optimization to ensure proper program execution and meaningful results, including appropriate time steps for ode45 and section plane definition parameters for accurate Poincare mapping.
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