Imperial College London

ProfessorDmitryTuraev

Faculty of Natural SciencesDepartment of Mathematics

Professor of Applied Mathematics & Mathematical Physics
 
 
 
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Contact

 

d.turaev

 
 
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Location

 

634Huxley BuildingSouth Kensington Campus

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Summary

 

Dynamics of Games - MATH96043

Aims

Contents of the module.
Recently there has been quite a lot of interest in modelling learning. The settings to which these models are
applied is wide-ranging. Examples are
(i) how populations in biology optimise their strategies and
(ii) how people pick what actions to take in a competitive environment.
This module is aimed at discussing a number of such models in which learning evolves over time, and which
have a game theoretic background. The module will use tools from the theory of dynamical systems, and will
aim to be rigorous. Topics will include replicator dynamics and best response dynamics.

Role

Lecturer

Bifurcation Theory - MATH96041

Aims


This course serves as an introduction to bifurcation theory, concerning the study of how the behaviour of dynamical systems (ODEs, maps) changes when parameters are varied.  The following topics will be covered:

1)     Bifurcations on a line and on a plane.

2)     Centre manifold theorem; local bifurcations of equilibrium states.

3)     Local bifurcations of periodic orbits – folds and cusps.

4)     Homoclinic loops: cases with simple dynamics, Shilnikov chaos, Lorenz attractor.

5)     Saddle-node bifurcations: destruction of a torus, intermittency, blue-sky catastrophe.

6)     Routes to chaos and homoclinic tangency.

 

Role

Lecturer

Dynamics of Games - MATH97181

Aims

 This module is aimed at discussing a number of such models in which learning evolves over time, and which
have a game theoretic background. The module will use tools from the theory of dynamical systems, and will
aim to be rigorous. Topics will include replicator dynamics and best response dynamics.

Role

Lecturer

Bifurcation Theory - MATH97177

Role

Lecturer

Dynamics of Games - MATH97069

Aims

This module is aimed at discussing a number of such models in which learning evolves over time, and which
have a game theoretic background. The module will use tools from the theory of dynamical systems, and will
aim to be rigorous. Topics will include replicator dynamics and best response dynamics.

Role

Lecturer

Bifurcation Theory - MATH97066

Aims


Role

Lecturer