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Social Dynamics and Emergence of Collective Behaviour

PGR-P-200

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Key facts

Type of research degree
PhD
Application deadline
Ongoing deadline
Country eligibility
International (open to all nationalities, including the UK)
Funding
Competition funded
Supervisors
Professor Mauro Mobilia
Schools
School of Mathematics
Research groups/institutes
Applied Mathematics
<h2 class="heading hide-accessible">Summary</h2>

Approaches relying on nonlinear dynamics and statistical mechanics have provided compelling models and crucial insights to understand interdisciplinary problems and emergent phenomena in complex systems. In the realm of social dynamics, one paradigmatic example is the voter model, where individuals in a population can be in one of two opinion states. The voter model is also closely related to evolutionary games used to model social and cooperation dilemmas. In this class of models, an individual is selected at random and adopts (with some probability) the state of its randomly-chosen neighbour; this update step is applied repeatedly. In this project, we propose to develop equally simple and paradigmatic individual-based models to investigate social behaviour like the emergence of conformity, polarization, or of multicultural states. For this, the dynamics will be implemented on various types of graphs whose topology generally evolves in time and is coupled with the dynamics of the agents occupying of the network. Here, we will study a series of opinion dynamics models using a well-rounded combination of mathematical methods, notably the theory of dynamical systems and differential equations, stochastic processes, and tools from statistical mechanics.

<h2 class="heading hide-accessible">Full description</h2>

<p>Particularly interesting questions will be related to the co-evolution of the nodes of the graphs (representing the agents&rsquo; opinions) and the links between them (modelling the agents&rsquo; connections) under social interactions such as <a href="https://journals.aps.org/pre/abstract/10.1103/PhysRevE.104.044311">homophily</a> or <a href="https://arxiv.org/abs/2107.13945">heterophily</a>. Examples of problems of interest are:</p> <p>(i) Consensus, group pressure and fanaticism: we will study the formation of consensus and the role of group pressure on conformism in voter-like models when the population is heterogeneous on adaptive networks. As an example of population heterogeneity, we will consider the influence of fanatical individuals (zealots) favouring a specific &quot;opinion&quot; on the system&#39;s fate for various types of dynamics (update rules). The models will be first studied on static graphs where nodes represent individuals with random connections that are random but do not evolve in time, and then on adaptive networks with coupled dynamics of nodes and links.</p> <p>(ii) Similar type of questions can be asked in the framework of evolutionary game theory for models, such as the prisoner&#39;s dilemma, that metaphorically describe social dilemmas and aim at studying the emergence of cooperative behaviour. We will be particularly interested in studying evolutionary games on adaptive networks.</p> <p>(iii) Dynamics of polarization: In many democracies, like in the UK, there are some major parties that trade governing roles every election and a number of other parties that access governing roles only very rarely. These can typically are prone to make compromise and alliances with parties of more extreme opinions, possibly leading to either societal polarization or fragmentation. We shall devise voter-like models to describe how polarization and marginalization emerge. We will typically study the probability for minority parties to reach the majority and the average time for such events to occur, and aim at characterizing the composition of the polarized states.</p> <p>Keywords: opinion dynamics, evolutionary games, complex systems, individual-based modelling, statistical mechanics, stochastic processes, stochastic simulations, networks, applied mathematics</p>

<h2 class="heading">How to apply</h2>

<p>Formal applications for research degree study should be made online through the&nbsp;<a href="https://www.leeds.ac.uk/info/130206/applying/91/applying_for_research_degrees">University&#39;s website</a>. Please state clearly in the Planned Course of Study section that you are applying for <em><strong>PHD Applied Mathematics FT</strong></em> and in the research information section&nbsp;that the research degree you wish to be considered for is <em><strong>Social Dynamics and Emergence of Collective Behaviour</strong></em>&nbsp;as well as <a href="https://eps.leeds.ac.uk/maths/staff/4064/professor-mauro-mobilia">Professor&nbsp;Mauro Mobilia</a> as your proposed supervisor.</p> <p>If English is not your first language, you must provide evidence that you meet the University&#39;s minimum English language requirements (below).</p> <p class="MsoNoSpacing"><strong><em>As an international research-intensive university, we welcome students from all walks of life and from across the world. We foster an inclusive environment where all can flourish and prosper, and we are proud of our strong commitment to student education. Across all Faculties we are dedicated to diversifying our community and we welcome the unique contributions that individuals can bring, and particularly encourage applications from, but not limited to Black, Asian, people who belong to a minority ethnic community, people who identify as LGBT+ and people with disabilities. Applicants will always be selected based on merit and ability.</em></strong></p> <p class="MsoNoSpacing"><strong>Applications will be considered on an ongoing basis. &nbsp;Potential applicants are strongly encouraged to contact the supervisors for an informal discussion before making a formal application. &nbsp;We also advise that you apply at the earliest opportunity as the application and selection process may close early, should we receive a sufficient number of applications or that a suitable candidate is appointed.</strong></p> <p><strong>Please note that you must provide the following documents in support of your application at the point you submit:</strong></p> <ul> <li><strong>Full Transcripts of all degree study or if in final year of study, full transcripts to date</strong></li> <li><strong>Personal Statement outlining your interest in the project</strong></li> <li><strong>CV</strong></li> </ul> <p>&nbsp;</p>

<h2 class="heading heading--sm">Entry requirements</h2>

Applicants to research degree programmes should normally have at least a first class or an upper second class British Bachelors Honours degree (or equivalent) in an appropriate discipline. The criteria for entry for some research degrees may be higher, for example, several faculties, also require a Masters degree. Applicants are advised to check with the relevant School prior to making an application. Applicants who are uncertain about the requirements for a particular research degree are advised to contact the School or Graduate School prior to making an application.

<h2 class="heading heading--sm">English language requirements</h2>

The minimum English language entry requirement for research postgraduate research study is an IELTS of 6.0 overall with at least 5.5 in each component (reading, writing, listening and speaking) or equivalent. The test must be dated within two years of the start date of the course in order to be valid. Some schools and faculties have a higher requirement.

<h2 class="heading">Funding on offer</h2>

<p><strong>Self-Funded or externally sponsored students are welcome to apply.</strong></p> <p><strong>UK&nbsp;</strong>&ndash;&nbsp;The&nbsp;<a href="https://phd.leeds.ac.uk/funding/209-leeds-doctoral-scholarships-2022">Leeds Doctoral Scholarships</a>, <a href="https://phd.leeds.ac.uk/funding/198-akroyd-and-brown-scholarship-2022">Akroyd &amp; Brown</a>, <a href="https://phd.leeds.ac.uk/funding/199-frank-parkinson-scholarship-2022">Frank Parkinson</a> and <a href="https://phd.leeds.ac.uk/funding/204-boothman-reynolds-and-smithells-scholarship-2022">Boothman, Reynolds &amp; Smithells</a> Scholarships are available to UK applicants. &nbsp;<a href="https://phd.leeds.ac.uk/funding/60-alumni-bursary">Alumni Bursary</a> is available to graduates of the University of Leeds.</p> <p><strong>Non-UK </strong>&ndash; The&nbsp;<a href="https://phd.leeds.ac.uk/funding/48-china-scholarship-council-university-of-leeds-scholarships-2021">China Scholarship Council - University of Leeds Scholarship</a>&nbsp;is available to nationals of China. The&nbsp;<a href="https://phd.leeds.ac.uk/funding/73-leeds-marshall-scholarship">Leeds Marshall Scholarship</a>&nbsp;is available to support US citizens.&nbsp; <a href="https://phd.leeds.ac.uk/funding/60-alumni-bursary">Alumni Bursary</a> is available to graduates of the University of Leeds.</p> <p>Please refer to the <a href="https://www.ukcisa.org.uk/">UKCISA</a> website for information regarding Fee Status for Non-UK Nationals starting from September/October 2021.</p>

<h2 class="heading">Contact details</h2>

<p>For further information about your application, please contact Doctoral College Admissions by email:&nbsp;<a href="mailto:EMAIL@leeds.ac.uk">m</a><a href="mailto:maps.pgr.admissions@leeds.ac.uk">aps.pgr.admissions@leeds.ac.uk</a>, or telephone: +44 (0)113 343 5057</p> <p>For further information about this project,&nbsp;please contact Dr Mauro Mobilia by email:&nbsp;<a href="mailto:M.Mobilia@leeds.ac.uk">M.Mobilia@leeds.ac.uk</a></p>


<h3 class="heading heading--sm">Linked research areas</h3>