Successful completion of the LUC 100 level course Mathematical Modelling.
Humans exploit their natural environment in many ways. This exploitation can become a driving force that ultimately determines the fate of biological resources. The interaction between ecological and socio-economical dynamics has often led to unforeseen catastrophic results. In some cases warning signs were present, but ignored for economic reasons, and disaster ensued.
The collaborative development of dynamical models by mathematicians, biologists, and economists provides a growing insight into the human and biological mechanisms that underlie ecosystem collapses. These models show which factors are crucial in determining the fate of ecosystems. They are used to examine the consequences of scenarios that are too risky, too costly, or simply impossible to study with practical experiments.
This is a course on how to build and study such models. We will study general patterns predicted by strategic models that capture the main features of socio-economic systems and ecosystems rather than detailed, complex models that can only be applied to particular situations. We focus on continuous-time dynamics, described by systems of differential equations, and put the emphasis on the conceptual basis of model building. The software package R is used to examine model dynamics numerically.
After successful completion of this course students should be able to:
Design, adjust, and refine dynamical models for interactive ecological and socio-economical dynamics.
Analyse models numerically with R, and (where possible) mathematically,
Interpret the results of models in their practical context,
Critically evaluate models.
After successful completion of this course students should know and understand:
Basic principles of continuous time dynamical models, such as different types of dynamics, analysis of local stability, bifurcation-, and phase plane plots
R code for programming functions, working with named lists and dataframes, and numerical analysis of ordinary differential equations
Examples of applications of dynamical models in the context of resource exploitation.
Once available, timetables will be published in the e-Prospectus.
Mode of instruction
Lectures, group-assignments and -discussions, class discussions.
Class participation: 5%
Quizzes (weeks 2 to 5) 40%
Individual assignment (week 6) 35%
Group project (Reading week) 20%
In accordance with article 4.8 of the Course and Examination Regulations (OER), within 30 days after the publication of grades, the instructor will provide students the opportunity to inspect their exams/coursework.
There is a no re-sit policy at Leiden University College.
There will be a Blackboard site available for this course. Students will be enrolled at least one week before the start of classes.
Lecture notes ‘Modelling Bioeconomic Dynamics’, by Patsy Haccou. These will be made freely available in Blackboard.
The textbook: ‘Mathematics for Global Challenges’, by Patsy Haccou, will serve as basic background information. This book can be downloaded for free, from: https://www.universiteitleiden.nl/binaries/content/assets/governance-and-global-affairs/luc/rc-office/mathematics_for_gc.pdf
The latest version of the textbook will also be made freely available in Blackboard.
This course is open to LUC students and LUC exchange students. Registration is coordinated by the Education Coordinator. Interested non-LUC students should contact firstname.lastname@example.org.
Dr. P. Haccou: email@example.com
Note that participants should have a sufficient proficiency and interest in mathematics, and be prepared to amend their mathematics skills when necessary. Students with poor mathematics skills are advised not to choose this course.
Recommended prerequisites: Calculus course