Numerical methods for solving systems of chaotic first-order differential equations

❖ Abstract

In my master’s program assignment for “Numerical Methods with Applications to Ordinary and Partial Differential Equations” I initially chose to solve the Lorenz chaotic equations and their extensions using numerical methods in Python due to my interest in cryptology. However, my project evolved to encompass solving all chaotic systems of first-order differential equations by creating a versatile Python script.

In the accompanying pdf, I summarized key facts about the Lorenz system and presented a generalized problem in Chapter 1, introduced three numerical methods in Chapter 2, and showcased the diverse and intriguing results obtained from solving the problem for various chaotic systems in Chapter 3.

❖ Files Included

• PDF (english)
• Interactive Python Notebook (english)
• Presentation (the presentation was continued showing animation from 2nd ipynb file)

❖ Keywords

Chaotic first-order differential equations, Lorenz system, chaotic cryptography, numerical analysis, Euler method, fourth-order Runge-Kutta, Generalized multidimensional Newton, 4d hyperchaotic Lorenz system, Chen system, Nose-Hoover Oscillator, Sprott-Jafari system