Simulating Duffing Oscillator in MATLAB ode45 and Python SciPy IVP | Computational Mechanics-Vid 01

In this video, we step into the world of nonlinear dynamics through learning about Georg Duffing and his work that led to Duffing oscillator, a classic example of a chaotic system. You will learn how to simulate and visualize this complex system using both MATLAB (ODE45) and Python (SciPy's solve_ivp).

🕒 Timestamps:
00:00 History, Background and Applications of Duffing Oscillator
02:09 Understanding the Duffing Equation
03:32 Newton's Second Law
04:10 Duffing Equation: General and Specific Forms
05:15 Formulating Duffing Equation for ode45 solver
06:29 Comparison of Matlab ode45 solver and Scipy integrate solve_ivp functions
08:02 MATLAB ode45 syntax and solve_ivp syntax for a simple differential equation
09:44 Walkthrough of Python code for solving Duffing equation
13:15 Interpreting sImulation results
14:18 Concluding remarks
📚 What You'll Learn:

Complete breakdown of the Duffing equation:
mx'' + γx' + αx + βx³ = Fcos(ωt)
Step-by-step implementation in both MATLAB and Python
Understanding chaos through sensitivity to initial conditions
Real-world applications and examples

🔧 Technical Details Covered:

ODE45 solver in MATLAB
SciPy's solve_ivp integration
Phase space visualization
Parameter effects on system behavior

💻 Code Available:
Get the complete source code for Python implementations at:
https://github.com/sraocodes/Compute-Stories/blob/main/Python/duffing.py

Get the complete source code for MATLAB implementations at:
https://in.mathworks.com/matlabcentral/fileexchange/174490-duffing-oscillator-phase-space-animator

🎯 This video is intended For:

Engineering students
Physics enthusiasts
Mathematics learners
Anyone interested in chaos theory and nonlinear dynamics

Видео Simulating Duffing Oscillator in MATLAB ode45 and Python SciPy IVP | Computational Mechanics-Vid 01 канала Compute Stories 💻