Important notice
The course guide is provisional.
The PDF version of the course guide may take a few days to become available in the DDD.
Dynamical Systems and Complexity
Code: 45559Credits: 6
| Degree programme | Type | Course |
|---|---|---|
| Modelling for Science and Engineering | OP | 1 |
Contact lecturer
- Name :
- Jordi Villadelprat Yague
- Email :
- jordi.villadelprat@uab.cat
Teaching staff
- Angel Calsina Ballesta
- Daniel Campos Moreno
Group languages
You can consult this information at the end of the document.
Prerequisites
Students must have mathematical skills at a graduate level of a scientific degree.
Objectives
The course aims to develop the students’ ability to systematically analyze deterministic nonlinear dynamical models and to elaborate mathematical models of real systems.
Learning outcomes
- CA09 (Devise models based on dynamical systems and complex systems to solve specific practical problems.) Devise models based on dynamical systems and complex systems to solve specific practical problems.
- CA10 (Communicate to an expert audience the results obtained from the analysis of models based on dynamic and complex systems incorporating ethical, sustainability and gender equality criteria.) Communicate to an expert audience the results obtained from the analysis of models based on dynamic and complex systems incorporating ethical, sustainability and gender equality criteria.
- CA11 (Assess, using specific metrics and mathematical tools, the level of complexity of a set of data obtained through experimentation and/or observations.) Assess, using specific metrics and mathematical tools, the level of complexity of a set of data obtained through experimentation and/or observations.
- KA09 (Recognise the main analysis techniques to study dynamical systems, as well as the theoretical scope of application of each of them.) Recognise the main analysis techniques to study dynamical systems, as well as the theoretical scope of application of each of them.
- KA10 (Recognise the different criteria that can be used to quantify and/or measure the complexity of a system.) Recognise the different criteria that can be used to quantify and/or measure the complexity of a system.
- SA09 (Formulate dynamical systems and complex models capable of capturing essential dynamic features of specific applications.) Formulate dynamical systems and complex models capable of capturing essential dynamic features of specific applications.
- SA10 (Solve, either analytically or computationally, complex dynamic models using the appropriate mathematical tools for each situation.) Solve, either analytically or computationally, complex dynamic models using the appropriate mathematical tools for each situation.
- SA11 (Implement tools and methodologies to study emerging behaviours in reference models in the field of complex systems.) Implement tools and methodologies to study emerging behaviours in reference models in the field of complex systems.
Contents
1. Introduction to Dynamical Systems
Types and characteristic properties. Related concepts.
2. One-Dimensional Discrete Dynamical Systems
Graphical and analytical study. Fixed points. Linear stability. Bifurcations. The logistic map.
3. Two-Dimensional Dynamical Systems
Classification of linear systems. Phase portrait. Limit cycles. Bifurcations. Biological models.
4. Chaotic Dynamical Behavior
Deterministic chaos. Definition. Examples.
5. Quasilinear first order Partial Differential Equations
The traffic flow model. Shock waves. Reaction diffusion equations. Morphogenesis.
6. Complexity
Systems with novel organized topology. Basic elements of complex systems. Emergent behaviors. Case studies. Measures of complexity.
Learning activities and methodology
| Title | Hours | ECTS | Learning outcomes |
|---|---|---|---|
| Problem sets and projects | 30 | 1.2 | CA09, CA10, CA11, KA09, KA10, SA09, SA10, SA11 |
| Theory and problem-solving classes | 48 | 1.92 | CA09, CA10, CA11, KA09, KA10, SA09, SA10, SA11 |
| Independent study | 66 | 2.64 | CA09, CA11, KA09, KA10, SA09, SA10, SA11 |
The methodology is based on lectures that include some practical exercises (either written or computational). Some of the exercises will be solved and submitted periodically by students through the Virtual Campus. Afterwards, any doubts regarding these exercises will be discussed in class.
Note: 15 minutes of one class session, within the schedule established by the department or degree program, will be reserved for students to complete surveys evaluating the teaching performance and the course/module.
Assessment
Continuous assessment activities
| Title | Weight | Hours | ECTS | Learning outcomes |
|---|---|---|---|---|
| Exam | 70% | 6 | 0.24 | CA09, CA11, KA09, KA10, SA09, SA10 |
| Projects and worked-out exercises | 30% | 0 | 0 | CA09, CA10, CA11, KA09, KA10, SA09, SA10, SA11 |
Continuous Assessment
Grades will be based on:
- Submission of solved problems, simulations, reports, and presentations, which will account for 30% of the final grade.
- Written exams, which will account for 70% of the final grade.
To pass the course, the weighted average of both components must be greater than 5 (out of 10).
Single Assessment
Students who choose the single assessment modality must take a final exam, which will consist of problem-solving and some theoretical questions. After the exam, they must also submit all exercises and reports related to the coursework. The final grade and the passing threshold are the same as in the continuous assessment.
For both types of assessment (continuous and single), if the final grade is below 5, the student will have a second opportunity to pass the course through a resit exam (worth 70%) and the submission of exercises and reports (worth 30%).
NOTE: In this course, the use of Artificial Intelligence (AI) technologies is not permitted at any stage. Any work that includes AI-generated fragments will be considered a breach of academic honesty and may result in a partial or total penalty on the activity grade, or more serious sanctions in cases of severe misconduct.
Bibliography
- S.H. Strogatz. Nonlinear Dynamics and Chaos. Second Edition. Perseus Books, Westview Press, Boulder, 2014.
- R.V. Solé y S.C. Manrubia, Orden y caos en sistemas complejos, ediciones UPC, Barcelona, 2001.
- S.H. Strogatz. SYNC. Rythms of nature, rythms of ourselves, Penguin, 2004.
- S. Parker , Leon O. Chua. Practical Numerical Algorithms for Chaotic Systems (1989).
- B.C. Goodwin, How the Leopard Changed Its Spots: Evolution of Complexity. Prentice Hall, 1994.
− Hanski, I. Metapopulation Ecology Oxford University Press. 1999.
− J.D. Murray. Mathematical Biology I: An introduction. Interdisciplinary Applied Mathematics 2002
− W. A. Strauss, Partial Differential Equations: An Introduction, John Wiley & Sons, 1992.
− K. Kaneko. Theory and Applications of Coupled Map Lattices (Nonlinear Science: Theory and Applications) 1st Edition, 1993
− A. Ilachinski. Cellular Automata: A Discrete Universe, 2001
− U. Dieckmann, R. Law, J.A.J. Metz. The Geometry of Ecological Interactions: Simplifying Spatial Complexity: 1 (Cambridge Studies in Adaptive Dynamics, Series Number 1), 2000
- R. Clark Robinson, An introduction to Dynamical Systems: Continuous and Discrete, Pure and Applied undergraduate texts, American Mathematical Society, 2012
- Robert L. Devaney, An introduction to Chaotic Dynamical Systems, Westview Press, 2003
- Stefan Thurner, Peter Klimek, Rudolf Hanel, Introduction to the Theory of Complex Systems, Oxford University Press, 2018
- Introduction to Complexity (online). Complexity Explorer, Santa Fe (https://www.complexityexplorer.org/courses/185-introduction-to-complexity#gsc.tab=0)
Software
There is no specific software for the subject.
Course groups and languages
The information provided is provisional until November 30. After this date, you will be able to consult the language of each group through this link. To access the information, you will need to enter the course CODE
| Type of teaching | Group | Language | Semester | Shift |
|---|---|---|---|---|
| (TEm) Theory (master) | 1 | English | first semester | morning-mixed |