This application is intended to introduce the tenets and application of Dynamical Systems Theory. Through providing a mix of background information and examples, the module will guide the user through defining fixed points in both one and two dimensional systems. The learning objectives are as follows:

1. Become Familiar with Dynamical Systems Theory

By the end of this notebook, you should be able to have a basic conceptual understanding of how Dynamical Systems Theory can be applied to a variety of scales and systems.

• You should understand what an equilibrium point is and why it is a special case in a system of equations. You should also be able to find equilibrium points in one and two dimensions.
• You should understand what the stability of an equilibrium point means and how to determine the stability of an equilibrium point in one and two dimensions.
• You should understand how equilibrium points and their stability determine the behavior of trajectories in a dynamical system.

2. Understand ODE Modeling in Various Contexts

You should understand how ordinary differential equations (ODE) can be used to model dynamical systems and how the previously described concepts are realized in ODE models. You should also have a handle on a couple of calculus and linear algebra tools are applied in ODE models.

3. Be able to use DST in python

You should be able to follow the python code in this notebook and implement it for your own purposes. The extension of the tools we provide here to your own applications is one of the most important features we hope to provide. You should also understand the connections between the code and the concepts as described above.

Any feedback or questions can be sent to edforb@iu.edu or cmcshaff@iu.edu. Happy modeling!

Researchers should cite this work as follows:

• Forbes Eden, Mcshaffrey, Connor (2022), "Characterizing Fixed Points in Dynamical Systems," https://nanohub.org/resources/dstfp. (DOI: 10.21981/HK6B-EQ91).

  BibTex | EndNote