Complex Systems - 2021 entry

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.

In this module, you will encounter a wide range of dynamical behaviours exhibited by complex systems in nature, society and technology. You will gain an understanding of the underlying mechanisms that lead to complex behaviour and how to model complex systems computationally. By gaining an understanding of the paradigms and methods of complexity science you will be well equipped to undertake further studies in this emerging discipline, which is vital to understanding our increasingly complex world.

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%.

Web-based and electronic resources:

• ELE – College to provide hyperlink to appropriate pages

Reading list for this module: