This repository contains my report on Nonlinear Dynamics and its corresponding files for Summer of Science conducted by Maths and Physics Club IIT Bombay.
Nonlinear Dynamics and Chaos is a blend of applied mathematics and physical modelling, spreading across scientific disciplines like a spider's intricate web. It has provided new theoretical and conceptual tools that allow us to capture, understand, and link together the surprisingly complex behaviours of simple systems. It offers some markedly different perspectives on chance and determinism in scientific explanations of phenomena, mechanical systems versus complex adaptive system, the concepts of dimensions and complexity, and basic notions of change and equilibria.
Here, we study the mathematics behind this topic and explore its application in various fields.
This report is divided into parts: One Dimensional Systems followed by Two Dimensional Systems then Higher Dimensional stuff and then Discrete Dynamical Systems. Next, we examine Stochastic Systems. On our way, we will look at corresponding Linear Systems to gain insight onto Nonlinear ones. Then, we explore Chaos and Fractals. Finally, I encourage you to look at Mathematical Models and their exciting results.
The Report can be viewed here.
This is the primary TeX file which is to be compiled to get the report.
This is the BibTeX file containing the references used by me.