Qualitative Mathematical Modelling of Complex Systems - 2016

Qualitative mathematical modelling will be introduced as a means to understand and predict the dynamics of complex biological and socio-economic systems.

The technique poses the question: if all we know of a system is the general nature of relationships between species and environmental and human variables, but not the precise intensity of these interactions, then what do we know?

It turns out that we know not everything, but quite a lot. Qualitative mathematical modelling describes complex systems through only the sign (0, +, -) of the effect or interaction between variables, and thus can easily include variables and processes that are important, yet difficult to measure.

Calculations of system stability and predictions of perturbation response proceed through analysis of the feedback properties of a system. While model predictions are imprecise, there are nonetheless rigorously derived and readily testable.


This approach leads to many interesting, practical, multidisciplinary, and surprisingly overlooked applications for research and natural resource management.

Coursework will be divided between lecture and use of modelling software (provided); students will need access to computer laptops (or share with a partner) and will work in groups on applied problems.

Programme information: 

Day 1: Monday
Pre-start check that everyone has software loaded (PowerPlay, Maple)

Teaching Sections

1. Introduction, History & Philosophy
2. Community Matrix & Defining Relevant Subsystem
3. Numeric Example of Community Matrix & PowerPlay Software
4. Modified Interactions & Split Variables
5. Modeling Building Examples with PowerPlay
6. Press Perturbations
7. Use of Software & Practice Examples

Day 2: Tuesday

8. Questions & Review
9. Meaning & Definition of Self-effects
10. Socio-economic & Biophysical Systems
11. Lyapunov Stability (Kinaesthetic Demonstration)
12. Life Expectancy Change
13. Practice Examples

Day 3: Wednesday

14. Questions & Review
15. Positive Feedback and Alternative States
16. New Applications & Advances
17. Practice Examples

Past course editions: 

This course is also taught in . Please, have a look at .

Number of hours: 


Course dates: 

Monday, June 13, 2016 to Wednesday, June 15, 2016




Institut de Ciències del Mar

Maximum number of places: 


Contact for further information: 

For additional information, please check our Contact section or get in contact directly with the Lecturer of this course.


Full price of this course is 270€. A reduced registration fee is applied for early registrations (45 days before the opening of the course).

Price: 270.00€

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