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The module builds on this theme.

  • Chaos: An Introduction to Dynamical Systems!
  • Below-ground interactions in tropical agroecosystems: concepts and models with multiple plant components?
  • Math -- Dynamical Systems and Chaos!

Learning objectives: The module should give the ability to know when to use deterministic nonlinear models to describe a real set of data and analyse its limitations and when to use it. Syllabus: The main reference is the part called Chaos in the Strogatz's book in the recommended texts below.

Spring 2016

The module is accompanied by a practical part where the students are given specific examples to simulate on the computer. Lorenz System and strange attractor: bifurcation diagram, Hopf bifurcation, transient chaos and strange attractor regions. The Lorenz map.

Evaluation Scheme

Attracting, repelling, neutral fixed points and periodic points. The logistic family as a model of population dynamics: period-doubling bifurcations, Feigenbaum's universality.

Dynamical Systems and Chaos: Iterated Functions Summary

Lyapunov exponents. Invariant Cantor sets and coding. Existence of periodic orbits: Sarkovski's Theorem, Transition graphs. Fractal dimension and fractals: box dimension, Hausdorff dimension, similarity dimension, pointwise and correlation dimension. Iterated Function Systems.

Additional reading:

Fractal basin boundaries. Strange attractors: baker's transformation. Sterk , Harry L. Modelling distributed computing workloads to support the study of scheduling decisions Paulo Henrique Ribeiro Gabriel , Rodrigo Fernandes de Mello. Stabilization of periodic orbits in discrete and continuous-time systems Thiago P. Dynamics of a hyperchaotic Lorenz System Ruy Barboza. References Publications referenced by this paper. Nonlinear Dynamics and Chaos J. Michael T. Thompson , Harris B.

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  • MT, Dynamical Systems, Course Information.
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Chaos - An Introduction to Dynamical Systems | Kathleen T. Alligood | Springer

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