Tutorial 1: Linear dynamical systems

# Tutorial 1: Linear dynamical systems

This tutorial covers the behavior of dynamical systems, systems that evolve in time, where the rules by which they evolve in time are described precisely by a differential equation.

Differential equations are equations that express the **rate of change** of the state variable 𝑥. One typically describes this rate of change using the derivative of 𝑥 with respect to time (𝑑𝑥/𝑑𝑡) on the left hand side of the differential equation: 𝑑𝑥𝑑𝑡=𝑓(𝑥). A common notational short-hand is to write 𝑥˙ for 𝑑𝑥𝑑𝑡. The dot means "the derivative with respect to time".

Overview of this tutorial:

- Explore and understand the behavior of such systems where 𝑥 is a single variable
- Consider cases where 𝐱 is a state vector representing two variables

Topics covered in this lesson

- One-dimensional differential equations
- Oscillatory dynamics
- Deterministic linear dynamics in two dimensions
- Stream plots

Prerequisites

Experience with Python Programming Language.

Back to the course