Dynamical Systems

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This seminar was given 26 February 2009 as part of the PhD seminar series organised by the School of Economics & Finance of the University of St Andrews. It addresses dynamical systems, stability, optimal control and differential games and their applications in Economics and Biology, in resource extraction in particular.

Videos are in WMV format. Handouts are PDF.

Morning video 1 (51 minutes) - Dr Cartigny's presentation begins with an introduction on optimal control. He first explains the basic monosectorial optimal growth model. He then introduces some mathematical concepts by studying the qualitative proprieties of the stationary equilibrium. Handouts: Opt growth and fishery 1

Morning video 2 (25 minutes) - Dr Cartigny develops the concepts related to the calculus of variations and turnpike theorems. He then starts to develop the concept of optimal management in fishery by introducing the standard case. Handout: fishery 1

Afternoon video 1 (38 minutes) - Dr Cartigny concludes the standard case and then studies systematically a variation of the standard case. Handout: fishery 2.

Afternoon video 2 (47 minutes) - Dr Cartigny presents a case study issued from his own research. He explains the optimal spatial distribution of small and large scale fisheries in Chile. He then concludes on viscosity solutions in singular cases thanks to the calculus of variations. Handouts: fishery 3 and viscosity

About the Speaker

Dr Pierre Cartigny is Director of the Joint Research Unit for Systems Analysis and Biometrics at INRA in Montpellier (France). He is Associate Professor at the Université de la Mediterranée (France) and Research Associate at GREQAM in Marseille (France). His research interests mainly focus on modelling, analysing and controlling dynamic systems of biological, agronomical or environmental interest. These systems rely on the theory of complex system defined by ordinary or partial differential equations and on optimal theory.