Nonlinear Dynamics & Pattern Formation

Wiki with Exercises, Notes, Hints, and a Feedback-Forum
Jürgen Vollmer, Uni Leipzig, SoSe2021

We will start on Thursday, April 5.

Notes of Seminars are available here

• Gregoire Nicolis. Introduction to Nonlinear Science (Cambridge UP, 1995)
• Ed Ott. Chaos in Dynamical Systems (Cambridge UP, 1993)
• Michael Cross, Henry Greenside. Pattern Formation and Dynamics in Nonequilibrium Systems (Cambridge UP, 2009)

Each week there will be a set of problems (see toolbar on the left). For each problem there will be a discussion page, and eventually we will discuss the solutions in the seminar. On request I also offer suggestions for further study.

For selected problems I will set up a Sage playground, where you can explore the solutions to a range of problems in theoretical mechanics based on interactive Sage templates.

^Set^ Date^Topic ^PDF ^ | 1| 2021 04 13| Qualitative Analysis|220 kB| | 2| 2021 04 20| Basics in Dynamical Systems|82 kB| | 3| 2021 04 27| 1D maps|90 kB| | 4| 2021 05 04| Fractals and Symbolic Dynamics|106 kB| | 5| 2021 05 11| 1D measures|85 kB| | 6| 2021 05 18| From 1D to 2D maps|79 kB| | 7| 2021 05 25| 2D maps and their stable/unstable manifolds|125 kB| | 8| 2021 06 02| From maps to flows| |

===== Participation ===== * extension of the wiki and requests for help * tips and tricks concerning issues with university emails, moodle, almaweb, this wiki, etc * general discussion, feedback, and information about you Three are discussion forms on these pages. Viable suggestions and solutions will be promoted from the discussion to Howtos in the main part of the pages. Regular contributors will earn the right to directly edit the pages. ===== Seminar Talks ===== * Frederik. - Chaos in the BZ reaction - Hamiltonian chaos in deep learning the rock–paper–scissors-game * Konstantin. Turing mechanism and the Schnakenberg system (maybe also chemical pattern formation?) * p. 88 ff * https://cbeentjes.github.io/files/Ramblings/PatternFormationSchnakenberg.pdf * Lenoard. Bifurcation analysis for the Swift-Hohenberg-eq (1D). * base in code and plots: https://rveltz.github.io/BifurcationKit.jl/dev/Swift-Hohenberg1d/#Swift-Hohenberg-equation-1d-(Automatic) * + possibly extended version: https://rveltz.github.io/BifurcationKit.jl/dev/tutorials2b/#The-Swift-Hohenberg-equation-on-the-GPU-(non-local)-1 * please also check out * PyDSTool * Marc R Roussel:Bifurcation analysis with AUTO * Robert. caustics

We will have the exams on

• on 10 August 2023