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Social Dynamics and Emergence of Collective Behaviour

PGR-P-200

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
Dr 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 &quot;voter model&quot;, 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 and we will study a series of nonlinear (deterministic and stochastic) problems 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>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 &quot;voter model&quot;, 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 and we will study a series of nonlinear (deterministic and stochastic) problems using a well-rounded combination of mathematical methods, notably the theory of dynamical systems and differential equations, stochastic processes, and tools from statistical mechanics.</p> <p>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. 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. Another question of considerable interest concerns opinion dynamics on adaptive networks, on which the opinion of individuals and the connections between are coupled and change in time.</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 research information section&nbsp;that the research degree you wish to be considered for is &lsquo;Social Dynamics and Emergence of Collective Behaviour&rsquo; as well as&nbsp;<a href="https://physicalsciences.leeds.ac.uk/staff/64/dr-mauro-mobilia">Dr 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><em>We welcome applications from all suitably-qualified candidates, but UK black and minority ethnic (BME) researchers are currently under-represented in our Postgraduate Research community, and we would therefore particularly encourage applications from UK BME candidates. All scholarships will be awarded on the basis of merit.</em></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-Funding Students</strong></p> <p><strong>Funding Eligibility</strong></p> <p><strong>UK/EU</strong> &ndash;&nbsp;Leeds Doctoral Scholarship Award paying Academic Fees and Maintenance matching EPSRC rate of &pound;15,009 per year for 3 years, School of Mathematics Scholarship award paying Academic Fees and Maintenance matching EPSRC rate of &pound;15,009 per year for 3 years.&nbsp; Alumni Bursary is available to previous University of Leeds graduates offering 10% discount on Academic Fees.</p> <p><strong>International Students</strong> &ndash;&nbsp;China Scholarship Council-University of Leeds Scholarship Award paying Academic Fees for 3 years,&nbsp;School of Mathematics Scholarship award paying Academic Fees for 3 years, Commonwealth Scholarship and Commonwealth Split Site Scholarships.&nbsp; Alumni Bursary is available to previous University of Leeds graduates offering 10% discount on Academic Fees.</p>

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

<p>For further information 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>


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