This module 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 module, you will explore and understand both modelling approaches. You will gain knowledge of the assumptions underlying these models, their limitations, and how they are derived. You will learn how to simulate and explore the dynamics of computational models, using a variety of examples mostly drawn from natural systems. At the end of the module, we will introduce basic recurrent neural networks as examples of dynamical systems with multiple timescales.

• Formal exam
• Programming assignment

• Blackboard
• Unconfirmed practical marks when available
• Exam Papers, past 2 years (where applicable)

• 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;
• to provide an understanding of the challenges of modelling complex systems across time and length scales.

By the end of this course the students should be able to:

• explain, critque and develop models of simple dynamical systems;
• write or extend code to simulate and visualize the dynamics of 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;
• independently review, develop and/or simulate approaches to modelling natural systems.

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).

Optional modules within the school have limited capacity. We will always try to accommodate all students but cannot guarantee a place.