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A 4D chaotic attractor written in different software's as part of a simulation assignment during my Masters on Mechatronics Engineering.
Introduction
Introduction
During my Master's first semester I had an assignment to design and model a 4D oscillator circuit using different commercial and non-commercial tools and software as well as learn and apply different mathematical methods to model, simulate and visualise 4D system.
Differential equations
Differential equations
Four ordinary differential equations were provided, one per plane axis as seen in the image. The system was modelled using 4 different methods:
Python
Excel
MATLAB code
MATLAB (Simulink)
Python
Python
Python Odeint Solver simulation.
Python Initial Value Problem (IVP) solver simulation.
4D Oscillator 3D Simulation on MATLAB ODE45.
4D Oscillator Slider Control Python Code.
Simulink 4D Oscillator system
Simulink X-Y Phase Diagram Result
Excel 4D Oscillator Simulation Using Euler's MethodÂ
Even thou it wasn't required for my assignment, I simulated other commonly known chaotic attractors and included a bifurcation analysis for all the 4D oscillator parameters as well.
Sprott Attractor
Lorenz Attractor
Chua's Attractor
Bifurcation Diagrams X-Y-Z Planes for A paramater, Oscillator becomes stable when A > 27.
Bifurcation Diagrams for X-Y-Z Planes for K parameter, Oscillator becomes stable when K > 25.
Conclusion
Conclusion
Thanks to this project, I have learned how to solve and simulate differential equations and chaotic oscillators using a different number of software such as as python and MATLAB and different mathematical methods such as the Euler method and Runge-Kutta. Unfortunately , I couldn't build a physical model of the system due to a lack of knowledge on analogue electronics, for this reason I have started a new personal project on my spare time to develop a simple Chua's oscillator circuit to better understand analogue electronics, when finished a will attempt at making another electronic model replicating the 4D oscillator which I had simulated.
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