MT4552 Population Dynamics Models in Mathematical Biology

Academic year

2024 to 2025 Semester 2

Further information on which modules are specific to your programme.

Key module information

SCOTCAT credits

15

The Scottish Credit Accumulation and Transfer (SCOTCAT) system allows credits gained in Scotland to be transferred between institutions. The number of credits associated with a module gives an indication of the amount of learning effort required by the learner. European Credit Transfer System (ECTS) credits are half the value of SCOTCAT credits.

SCQF level

SCQF level 10

The Scottish Credit and Qualifications Framework (SCQF) provides an indication of the complexity of award qualifications and associated learning and operates on an ascending numeric scale from Levels 1-12 with SCQF Level 10 equating to a Scottish undergraduate Honours degree.

Availability restrictions

Not automatically available to General Degree students

Planned timetable

9.00 am Mon (even weeks), Tue and Thu

This information is given as indicative. Timetable may change at short notice depending on room availability.

Module coordinator

Dr J Kursawe

Dr J Kursawe
This information is given as indicative. Staff involved in a module may change at short notice depending on availability and circumstances.

Module description

This module will explore real world applications of mathematics to biological problems e.g. harvesting of fish stocks, host-parasitoid systems, predator-prey dynamics, molecular interactions. The mathematical techniques used in the modelling will be nonlinear difference equations and ordinary differential equations. The module will be useful to students who wish to specialise in Applied Mathematics in their degree programme.

Relationship to other modules

Pre-requisites

BEFORE TAKING THIS MODULE YOU MUST PASS MT3504

Assessment pattern

Written Examination = 80%, Coursework = 20%

Re-assessment

Oral examination = 100%

Learning and teaching methods and delivery

Weekly contact

2.5 lectures (x 10 weeks) and 1 tutorial (x 10 weeks).

Scheduled learning hours

35

The number of compulsory student:staff contact hours over the period of the module.

Guided independent study hours

115

The number of hours that students are expected to invest in independent study over the period of the module.

Intended learning outcomes

  • Understand how to apply mathematical models to various problems arising in population dynamics and how to analyse and interpret these models
  • Undertake a stability analysis of continuous time, nonlinear ordinary differential equation models (including delay systems) for single and interacting species
  • Understand the concept of a Hopf bifurcation and how it applies to predator-prey systems and their oscillatory dynamics
  • Understand and implement the technique of singular perturbation theory and matched asymptotic expansions applied to models of enzyme kinetics
  • Undertake a stability analysis of discrete time, nonlinear difference equation models (including delay systems) for single and interacting species
  • Understand the concepts of periodic solutions of nonlinear difference equations, bifurcation, period-doubling and chaotic dynamics