Dynamical Systems and Fractals

Dynamical Systems and Fractals

Lecture notes from an Oklahoma State University course on symbolic and analytic dynamics, with an overview of fractal geometry.

Dynamics of Physical Systems; Chaos, Fractals, and Dynamical Systems

Dynamics of Physical Systems; Chaos, Fractals, and Dynamical Systems

The set of lectures is aimed at addressing this pedagogical issue, and is divided into two parts. In the first part, the readers are introduced to the methods and techniques for translating a physical problem into mathematical language by formulating differential equations. In general, the...

Emerging Behavior and Spatiotemporal Chaos in Reaction-Diffusion Models: GPU-accelerated simulations in a web browser over the internet

Emerging Behavior and Spatiotemporal Chaos in Reaction-Diffusion Models: GPU-accelerated simulations in a web browser over the internet

A set of interactive programs to study and analyze several models of excitable media in tissue. As the waves they produce propagate through the media, the models exhibit complex spatiotemporal dynamics that cannot be appreciated from an analysis of the underlying equations or even verbal...

Graduate (MAGIC) course Dynamical Systems II: Maps

Graduate (MAGIC) course Dynamical Systems II: Maps

Access course material through the website. The material was used to deliver the module MAGIC060 online via "Access Grid" technology. The course was developed originally by Toby Hall and taught in 2013 by Lasse Rempe-Gillen, on behalf of the EPSRC-funded MAGIC (Mathematics Access Grid...

Graduate (MAGIC) course Dynamical Systems: Flows

Graduate (MAGIC) course Dynamical Systems: Flows

These are lecture notes (slides) for a 10-hour course delivered as part of the MAGIC suite of graduate-level courses in nonlinear dynamics and dynamical systems. The course was all about flows; there is a follow-on course on maps and another on equivariant bifurcation theory. Topics covered...

Graduate (MAGIC) course Equivariant Bifurcation Theory

Graduate (MAGIC) course Equivariant Bifurcation Theory

These are course materials for a ten lecture course for first year PhD students in mathematics. It is not aimed necessarily at those who will specialise or use Equivariant Bifurcation Theory, but it is designed to be a “broadening” training for example for those doing more...

Graduate (MAGIC) Course on Ergodic Theory

Graduate (MAGIC) Course on Ergodic Theory

Prize winner, Teaching DS Competition, 2013

These notes form a 10-lecture course on ergodic theory and its applications to hyperbolic dynamical systems. The level of material is suitable for beginning graduate students in mathematics who want to either gain an overview of various aspects of ergodic theory, or want to gain a more detailed...

Graduate course on dynamical systems

Graduate course on dynamical systems

Prize winner, Teaching DS Competition, 2013

Course materials for two-quarter (20 week) graduate course on dynamical systems. (Advanced undergraduates have successfully taken the course.) The courses integrate nonlinear dynamics (low- and high-dimensional systems), symbolic dynamics, information theory, and computation theory. The theme,...

Graduate Introductory Survey Course on Nonlinear Dynamics

Graduate Introductory Survey Course on Nonlinear Dynamics

A web site for a graduate introductory survey course on nonlinear dynamics, originally intended for physical science students, but also appropriate for mathematics students with no prior background. The web site includes detailed lecture notes, xppaut input files to illustrate certain...

Interactive Materials for Teaching Elementary Dynamical Systems

Interactive Materials for Teaching Elementary Dynamical Systems

Prize winner, Teaching DS Competition, 2013

The web site Math Insight contains expository material, interactive applets, videos, and exercises intended to be used either in a classroom setting or as an online resource for the greater community. The focus is on qualitative description rather than getting all technical details precise. Many...

Introductory Computational Neuroscience

Introductory Computational Neuroscience

These materials are a work in progress that can be used as the basis of an introductory computational neuroscience course that is intended to be a roughly 60/40 mixture of hands-on lab work and lecturing. The original one semester, 3 credit hour...

nonlinear dynamics 1: geometry of chaos

nonlinear dynamics 1: geometry of chaos

An advanced, semester length introduction to nonlinear dynamics, with emphasis on methods used to analyze chaotic dynamical systems encountered in science and engineering. The theory developed here (that you will not find in any other course :) has much in common with (and complements)...

Nonlinear dynamics and Chaos: Lab Demonstrations

Nonlinear dynamics and Chaos: Lab Demonstrations

This 1994 video shows six laboratory demonstrations of chaos and nonlinear phenomena, intended for use in a first course on nonlinear dynamics. Steven Strogatz explains the principles being illustrated and why they are important. The demonstrations are: (1) A tabletop waterwheel that is an...

One Dimensional Dynamics

One Dimensional Dynamics

See here for an explanation of the software and sample lab assignment using it. One-dimensional maps are the simplest dynamical systems that may be chaotic. Textbooks can give a static picture of such dynamics, but since dynamics involves time, a student can get a much better understanding of...

Path Integral Methods for Stochastic Differential Equations

Path Integral Methods for Stochastic Differential Equations

A pedagogical paper (Path Integral Methods for Stochastic Differential) on how to use path integral and diagrammatic methods to solve stochastic differential equations perturbatively. The paper was originally written as a companion to a lecture by Carson Chow on the same topic at the 2009...

Peixoto’s Structural Stability Theorem: The One-dimensional Version

Peixoto’s Structural Stability Theorem: The One-dimensional Version

This paper describing how Peixoto's Structural Stability Theorem could be incorporated into an undergraduate class. Peixoto’s structural stability and density theorems represent milestones in the modern theory of dynamical systems and their applications. Despite the importance of these...

Review Articles Assignment in Ordinary Differential Equations

Review Articles Assignment in Ordinary Differential Equations

Several years ago, I started working with a new graduate student, who was richly decorated with all sorts of academic awards, local and national, for his academic achievements in mathematics. He was an excellent researcher, brilliant mathematician, and gifted student. I was therefore stunned to...

Synched Software

Synched Software

This file describes the Synched software and includes citations to related works. Synched is a piece of software that allows any user, ranging from a dynamical systems student exploring synchronization for the first time to a senior researcher presenting at a conference, to simulate and...

The Dynamical Systems and Technology Project at Boston University

The Dynamical Systems and Technology Project at Boston University

Part of an NSF sponsored program to help secondary school and college teachers of mathematics bring contemporary topics in mathematics (chaos, fractals, dynamics) into the classroom, and to show them how to use technology effectively in this process. Contains interactive papers and java applets...

The Math of Patterns

The Math of Patterns

Prize winner, Teaching DS Competition, 2013

The goal of this project is to provide a series of multimedia web resources that can supplement a course in dynamical systems. Motivated through several courses at Princeton and Oxford universities based on dynamical systems, differential equations, biology, and neuroscience, I sought to create...

The World of Bifurcation

The World of Bifurcation

A database of bifurcation problems and examples with a tutorial on nonlinear phenomena.

RSS