Modélisation géographique
[GEO2130]
[30h + 30h] 5 credits
Teacher(s): Eric Deleersnijder, Eric Deleersnijder(supplée N.), Sophie Vanwambeke
Language: French
Level: Second
Aims
-spatio-temporal analysis
-dynamic approaches that use differential equations
-fractals
The competences to be acquired during the course include :
-complex analyses using GIS
-use of softwares for modelling dynamic systems
-mathematical methods in geography
Main themes
GIS models
Simple spatio-temporal models
Diffusion models based on the logistic curve (migration and innovation)
Neighbourhood spatio-temporal models
Game of life
Cellular automata applied to urbanization and periurbanization
Hägerstrand 'revisited'
Transport models
Transport demand
Variational inequalities
Differential models
Introduction
State variables, parameters
Initial conditions, boundary conditions, etc
Linear ordinary differential problems
General solutions
Equilibrium points (stability, instability, oscillations)
Conservation/dissipation of energy (in a broad sense)
Example (Mururoa Lagoon)
Non-linear ordinary differential problems
Equilibrium points (stability, instability, oscillations)
Conservation/dissipation of energy (in a broad sense)
Qualitative notions of bifurcation
Qualitative notions on chaos and predictability
Examples (logistic model, prey-predator model, etc.)
Space- and time-dependent models
Partial differential problems
Integral properties
Box-model approximations
Example (Exxon Valdez oil spill, Alaska)
Parameter optimisation, validation and sensitivity analysis
Systems analysis in Geography
Self-organisation in human systems
Dynamic of urban centres
Intra-urban model
Case study : modelling the evolution of the United States (1950-1970)
Other information (prerequisite, evaluation (assessment methods), course materials recommended readings, ...)
GEO1342 - Geographical Information Systems
GEO1341 - Statistical modelling
Mathematics