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Unit of study_

CSYS5040: Criticality in Dynamical Systems

Semester 2, 2023 [Normal evening] - Camperdown/Darlington, Sydney

Criticality is one of the most important properties of Complex Systems. Criticality occurs in two related but distinct ways: 1. when a system unexpectedly collapses from one state to another, very different, state and 2. when a system is in a state with wild fluctuations and it is highly sensitive to small changes in behaviours. In the first case we call it a 'Tipping Point' and in the second case a 'Continuous Critical Transition'. There are many practical examples of these types of behaviour: Financial markets are often in a continuous critical transition and they can also quickly collapse, diseases that are transferred through a social network can suddenly explode into a pandemic, and a local power outage in an electricity network can cause entire cities to blackout. We will also look at selforganised criticality, where a system evolves to be near one of these 'dangerous' critical points, this is one of the most exciting emergent phenomena in modern applied sciences, engineering and business and we will cover present several real-world applications in this area. This unit will study a range of important examples in which criticality plays a key role and we will show what the underlying causes are for these uncontrolled collapses and wild dynamics. We will use a combination of software examples (Matlab) and mathematical techniques in order to illustrate when and how such interactions might occur and how to simulate their dynamics. It will cover crossdisciplinary concepts and methods based on nonlinear dynamics, including elements of chaos theory and statistical physics, such as fractals and percolation.

Unit details and rules

Unit code CSYS5040
Academic unit Computer Science
Credit points 6
Assumed knowledge

Mathematics at first-year undergraduate level. Some familiarity with mathematical and computational principles at an undergraduate university level (for example, differential calculus or linear algebra). Familiarity with a programming language at a beginners level for data analysis

Available to study abroad and exchange students


Teaching staff

Coordinator Michael Harre,
Type Description Weight Due Length
Assignment Literature Review
Written report
15% Week 03
Due date: 20 Aug 2023 at 23:59
Outcomes assessed: LO1 LO3 LO5
Assignment Programming for criticality:
Answers to programming questions
25% Week 07
Due date: 17 Sep 2023 at 23:59
Outcomes assessed: LO1 LO4 LO6
Assignment Dynamics and criticality project presentation
Oral report (or video) on a large scale project
20% Week 11
Due date: 29 Oct 2023 at 23:59
Outcomes assessed: LO1 LO2 LO3 LO4 LO5 LO6
Assignment Dynamics and criticality project final report
Final report on a significant piece of data analysis
40% Week 13
Due date: 05 Nov 2023 at 23:59
Outcomes assessed: LO1 LO2 LO3 LO4 LO5 LO6

Assessment summary

Literature review: You will write a short appraisal of an article or report which provides an information-theoretic analysis of empirical data, and critically evaluate that study. The reviews will be socially shared and discussed in class.

Programming for criticality: You will demonstrate your understanding of and ability to apply the techniques of dynamical systems theory and criticality. This will be based on using a simple model discussed in class.

Dynamics and criticality project presentation and report: You will develop a model for a real world application in which criticality may play a role in the dynamical evolution of the system. You will research the application area (brief literature review), develop a theoretical model, code the model in either Matlab or Mathematica, simulate the system both in and out of the critical phase of the system, analyse your results, and discuss the relevance of criticality to your system. You will deliver an in-class presentation, and write a report, describing your approach, the results, discussing implications for the system under study, and critically evaluating your findings.

Assessment criteria

The University awards common result grades, set out in the Coursework Policy 2014 (Schedule 1).

As a general guide, a high distinction indicates work of an exceptional standard, a distinction a very high standard, a credit a good standard, and a pass an acceptable standard.

Result name

Mark range


High distinction

85 - 100



75 - 84



65 - 74



50 - 64



0 - 49

When you don’t meet the learning outcomes of the unit to a satisfactory standard.

For more information see

For more information see guide to grades.

Late submission

In accordance with University policy, these penalties apply when written work is submitted after 11:59pm on the due date:

  • Deduction of 5% of the maximum mark for each calendar day after the due date.
  • After ten calendar days late, a mark of zero will be awarded.

Academic integrity

The Current Student website  provides information on academic integrity and the resources available to all students. The University expects students and staff to act ethically and honestly and will treat all allegations of academic integrity breaches seriously.  

We use similarity detection software to detect potential instances of plagiarism or other forms of academic integrity breach. If such matches indicate evidence of plagiarism or other forms of academic integrity breaches, your teacher is required to report your work for further investigation.

You may only use artificial intelligence and writing assistance tools in assessment tasks if you are permitted to by your unit coordinator, and if you do use them, you must also acknowledge this in your work, either in a footnote or an acknowledgement section.

Studiosity is permitted for postgraduate units unless otherwise indicated by the unit coordinator. The use of this service must be acknowledged in your submission.

Simple extensions

If you encounter a problem submitting your work on time, you may be able to apply for an extension of five calendar days through a simple extension.  The application process will be different depending on the type of assessment and extensions cannot be granted for some assessment types like exams.

Special consideration

If exceptional circumstances mean you can’t complete an assessment, you need consideration for a longer period of time, or if you have essential commitments which impact your performance in an assessment, you may be eligible for special consideration or special arrangements.

Special consideration applications will not be affected by a simple extension application.

Using AI responsibly

Co-created with students, AI in Education includes lots of helpful examples of how students use generative AI tools to support their learning. It explains how generative AI works, the different tools available and how to use them responsibly and productively.

WK Topic Learning activity Learning outcomes
Week 01 Introduction: The Old School meets New Schools of Thought Lecture (3 hr) LO1
Week 02 Introduction to fractals and chaos Lecture (3 hr) LO1 LO4
Week 03 Financial Markets Lecture (3 hr) LO2 LO3
Week 04 Decision Theory: Using Stochastic Equations Lecture (3 hr) LO3 LO4
Week 05 Artificial Intelligence: Predicting chaotic time series Lecture (3 hr) LO4 LO6
Week 06 Recurrence plot analysis and stability theory Lecture (3 hr) LO4 LO5 LO6
Week 07 Workflow for Criticality and Complex Time Series Analysis Lecture (3 hr) LO2 LO3
Week 08 Tipping Points and Bifurcations Guest Lecture Lecture (3 hr) LO4 LO5
Week 09 Distortions in Potential Functions Lecture (3 hr) LO4 LO5 LO6
Week 10 Complexity in housing markets + S&P500 Lecture (3 hr) LO4 LO6
Week 11 Bifurcations in the Social Ising Model Lecture (3 hr) LO2 LO3
Week 12 Computing social clustering, final report prep Lecture (3 hr) LO2 LO3 LO6
Week 13 Summary and wrap up, final report prep Lecture (3 hr) LO1 LO2 LO3 LO4 LO5 LO6

Study commitment

Typically, there is a minimum expectation of 1.5-2 hours of student effort per week per credit point for units of study offered over a full semester. For a 6 credit point unit, this equates to roughly 120-150 hours of student effort in total.

Required readings

All readings for this unit can be accessed through the Library eReserve, available on Canvas.

  • Title: Phase Transitions 

    Author: Solé, Ricard

    Publihed: 2011


    Phase transitions--changes between different states of organization in a complex system--have long helped to explain physics concepts, such as why water freezes into a solid or boils to become a gas. How might phase transitions shed light on important problems in biological and ecological complex systems? Exploring the origins and implications of sudden changes in nature and society, Phase Transitions examines different dynamical behaviors in a broad range of complex systems. Using a compelling set of examples, from gene networks and ant colonies to human language and the degradation of diverse ecosystems, the book illustrates the power of simple models to reveal how phase transitions occur. Introductory chapters provide the critical concepts and the simplest mathematical techniques required to study phase transitions. In a series of example-driven chapters, Ricard Solé shows how such concepts and techniques can be applied to the analysis and prediction of complex system behavior, including the origins of life, viral replication, epidemics, language evolution, and the emergence and breakdown of societies. Written at an undergraduate mathematical level, this book provides the essential theoretical tools and foundations required to develop basic models to explain collective phase transitions for a wide variety of ecosystems.

  • Didier Sornette, Critical Phenomena in Natural Sciences Chaos, Fractals, Selforganization and Disorder: Concepts and Tools.

Learning outcomes are what students know, understand and are able to do on completion of a unit of study. They are aligned with the University's graduate qualities and are assessed as part of the curriculum.

At the completion of this unit, you should be able to:

  • LO1. understand and extend the design of a model of critical dynamics using techniques from class and your own readings
  • LO2. take a set of data and apply the techniques developed in class in order to answer key questions about a system's evolution in a structured and rigorous fashion
  • LO3. understand models of dynamical systems, the nature of the time series they generate, be able to compare them with real time series data sets, and apply these simulations in order to understand the underlying mechanisms that drive the behaviour of complex systems over time
  • LO4. develop scientific programming skills that can be applied to the analysis of dynamical systems and critical phenomena
  • LO5. assess the nature of a system from its behaviour and make an informed decision as to whether it is 'critical' or not
  • LO6. simulate the critical behaviour of a system and decide whether or not the simulation matches the behaviour of the system.

Graduate qualities

The graduate qualities are the qualities and skills that all University of Sydney graduates must demonstrate on successful completion of an award course. As a future Sydney graduate, the set of qualities have been designed to equip you for the contemporary world.

GQ1 Depth of disciplinary expertise

Deep disciplinary expertise is the ability to integrate and rigorously apply knowledge, understanding and skills of a recognised discipline defined by scholarly activity, as well as familiarity with evolving practice of the discipline.

GQ2 Critical thinking and problem solving

Critical thinking and problem solving are the questioning of ideas, evidence and assumptions in order to propose and evaluate hypotheses or alternative arguments before formulating a conclusion or a solution to an identified problem.

GQ3 Oral and written communication

Effective communication, in both oral and written form, is the clear exchange of meaning in a manner that is appropriate to audience and context.

GQ4 Information and digital literacy

Information and digital literacy is the ability to locate, interpret, evaluate, manage, adapt, integrate, create and convey information using appropriate resources, tools and strategies.

GQ5 Inventiveness

Generating novel ideas and solutions.

GQ6 Cultural competence

Cultural Competence is the ability to actively, ethically, respectfully, and successfully engage across and between cultures. In the Australian context, this includes and celebrates Aboriginal and Torres Strait Islander cultures, knowledge systems, and a mature understanding of contemporary issues.

GQ7 Interdisciplinary effectiveness

Interdisciplinary effectiveness is the integration and synthesis of multiple viewpoints and practices, working effectively across disciplinary boundaries.

GQ8 Integrated professional, ethical, and personal identity

An integrated professional, ethical and personal identity is understanding the interaction between one’s personal and professional selves in an ethical context.

GQ9 Influence

Engaging others in a process, idea or vision.

Outcome map

Learning outcomes Graduate qualities

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