This module will probe new developments in complex systems modelling. The current era of big, complex and diverse datasets necessitates the development and understanding of complex system models. In this module, you will explore how simple rule-based inter-connected systems can give rise to enormous complexity in natural and man-made systems. Informed by practical examples, you will learn concepts from nonlinear dynamics such as chaos and bifurcation in deterministic and stochastic systems, fractal geometry, complex networks, emergence in cellular automata, self-organization, adaption, feedback loops, random fields and cascaded failures. Using state-of-the-art scientific computing software, you will simulate and develop your understanding of the nonlinear and often chaotic behaviours of weather sciences, interconnected power systems and financial systems; and visualise the real-life patterns found in remote sensing images of coastlines, plant leaves, animal skins and chemical reactions.

 

Prerequisites: MTHM607; Students should also have a general understanding of dynamical systems and differential equations at undergraduate level.

 

 

The module is structured in three blocks in which a specific topic is introduced and explored through computer labs. The topics may vary over time to reflect the most up to date research and educational practice. Examples of the material to be covered include:

 

Nonlinear Dynamics

Hamiltonian Systems

Dissipative Systems

Bifurcations

Chaos and Strange Attractors

 

Fractal Geometry

Understanding fractal geometry

Fractals arising from mathematical models and nature

 

Emergence and self-organisation

Cellular Automata

Agent Based Models

 

Complex Networks

Network Models

Networked Dynamical Systems (e.g. Synchronisation, Neural Networks)

 

Stochastic Systems

Statistical Physics

Criticality

Optimisation (e.g. Genetic Algorithms, Simulated Annealing)

 

Game Theory

Cooperation and Conflict

Nash Equilibria

 

Deferral – if you miss an assessment for certificated reasons judged acceptable by the Mitigation Committee, you will normally be either deferred in the assessment or an extension may be granted. The mark given for a re-assessment taken as a result of deferral will not be capped and will be treated as it would be if it were your first attempt at the assessment.

 

Referral – if you have failed the module overall (i.e. a final overall module mark of less than 50%) you will be required to resubmit the original assessment as necessary. The mark given for a re-assessment taken as a result of referral will be capped at 50%.