Teacher(s)
Deleersnijder Eric ;
Vanwambeke Sophie ;
Main themes
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
Spatial modelling
Self-organisation in systems
Cellular automata
Agent-based models
Examples are taken in physical geography, natural resource management and use, spatial epidemiology, history of land use
Modelling techniques
UML as an aid to conceptual modelling
Model evaluation: sensitivity, uncertainty, validation
Measuring landscape structure
Aims
Extend knowledge of modelling techniques focusing on geographical processes. More specifically, models based on:
-spatio-temporal analysis
-dynamic approaches that use differential equations
-landscape indices and fractals
The competences to be acquired during the course include:
-complex spatial analyses
-use of softwares for modelling dynamic systems
-mathematical methods in geography
The contribution of this Teaching Unit to the development and
command of the skills and learning outcomes of the programme(s) can be
accessed at the end of this sheet, in the section entitled
“Programmes/courses offering this Teaching Unit”.
Content
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
Prerequisites GEO1342 - Geographical Information Systems GEO1341 - Statistical modelling Mathematics
All lectures are in English. The course material and practical notes are in English and French
Program title
Sigle
Credits
Prerequisites
Aims
Master [120] in Forests and Natural Areas Engineering
Master [120] in Agriculture and Bio-industries
Master [120] in Agricultural Bioengineering
Master [120] in Environmental Bioengineering
Master [60] in Geography : General
Master [120] in Chemistry and Bioindustries
Master [120] in Geography : General