COM3001 Modelling and Simulation of Natural Systems
|| This unit will provide a practical introduction to
techniques used for modelling and simulating dynamic natural
systems. Many natural systems can be modelled appropriately
using differential equations, or individual based methods.
In this unit, students will explore and understand both
modelling approaches. They will gain knowledge of the
assumptions underlying these models, their limitations, and
how they are derived. Students will learn how
to simulate and explore the dynamics of computational
models, using a variety of examples mostly drawn from natural
systems. Students should be aware that there are limited places available on this course.
- Formal exam, group assignment
||Dr Aditya Gilra
- to extend mathematical and computational skills for studying dynamical systems;
- to enable understanding, analysis and construction of individual based and differential equations based models of dynamical systems, while appreciating their advantages and limitations;
- to provide practical knowledge of schemes for the simulation of individual based and differential equations based models;
- to introduce the application of individual based and differential equations based models to biological systems;
- to provide experience in developing interdisciplinary teamwork skills.
||By the end of this course the students should be able to:
- explain, critique and develop individual based and differential equations based models of simple dynamical systems;
- write or extend code to simulate and visualize the dynamics of individual based and differential equations based models, employing appropriate numerical methods;
- analyse mathematically the stability properties of simple dynamical systems;
- appraise applications of different modeling paradigms in the simulation of simple biological systems, while appreciating the benefits and limitations of each approach
- work productively in a team with members from potentially different academic backgrounds;
||The main focus of the module will be on the use of
differential equations and individual based models to
simulate the behaviour of natural systems. A number of
specific topics will be introduced that will be updated to
reflect recent developments, e.g.
- population dynamics
- physiological processes
||Prerequisites for this module are programming proficiency (preferably in MATLAB or Python) and A-level Mathematics (or equivalent).
||The course will consist of two 50 minute sessions per
week, either lectures or computer practicals, with an
additional 50 minutes lab session, tutorial or self organised group meeting.
||Students will receive feedback via lab sessions, written or verbal feedback at the group assignment description stage, written feedback on submitted assignments, and/or individual or group feedback on request.
- Programming for Computations - Python, 2nd Edition 2020, by Linge and Langtangen, Springer Open Access ebook.
- Programming for Computations - MATLAB/Octave, 1st Edition 2016, by Linge and Langtangen, Springer Open Access ebook.
- Chapters 22, 23 and 24 from "Applied Numerical Methods with MATLAB for Engineers and Scientists", 4th Edition 2018, by Chapra.
- A selection from Chapters 1, 11 and 14, "Differential
Equations, Dynamical Systems & An Introduction to
Chaos", 2nd Edition 2004 or 3rd Edition 2013, by Hirsch, Smale and Devaney.
- Chapter 1 of "Neuronal Dynamics" by Gerstner, Kistler, Naud and Paninski.
- Various published examples to be recommended during the module.