Prof. James P. Gleeson

(PhD, Applied Math, Caltech, 1999)

MACSI, Department of Mathematics and Statistics,

University of Limerick, Ireland

Telephone: +353 61 202634      Fax: +353 61 334927 

Email:      Twitter: @gleesonj

Office: B3051, Main Building, UL




My group works on mathematical models for stochastic dynamics, particularly on complex networks. As co-director of MACSI, I am also interested in applying mathematical tools and techniques to solving real-world problems, in collaboration with partners from industry, science and engineering. Our research is funded by Science Foundation Ireland and by the FET-Proactive scheme of the European Commission’s FP7.

My Google Scholar page is .



·         Course director MSc in Mathematical Modelling

·         MS6011: Advanced Methods I

·         MB4005: Analysis

·         MS4028: Stochastic differential equations for finance




·         I’m an invited speaker at NetSci 2014, Berkeley, June 2014.

·         We analyse a simple model of information diffusion on Twitter-like networks to show that competition between memes poises the system at criticality: Gleeson JP, Ward JA, O’Sullivan KP, Lee WT, “Competition-induced criticality in a model of meme popularity”, Phys. Rev. Lett. 112, 048701 (2014) ; arXiv:1305.4328. This paper was selected for a Synopsis article in APS Physics. Code for numerically calculating the probability generating functions, and implementing the FFT-based inversion, is available from Kevin O’Sullivan’s webpage.

·         I am an Associate Editor of the Journal of Complex Networks (Oxford University Press).

·         Octave/MATLAB code for solving the differential equations arising from the approximate master equations, pair approximations, and mean-field theories discussed in [Gleeson JP, Phys. Rev. Letters, 107, 068701 (2011)] and [Gleeson JP, Phys. Rev. X, 3, 021004 (2013)]  is now available for download from here. Comments and bug reports are welcome.


Recent and upcoming presentations:

·         Invited speaker at NetSci 2014, Berkeley, June 2014.

·         Invited seminar: Hamilton Institute, NUI Maynooth, 19 Mar 2014.

·         Invited seminar: Bristol Centre for Applied Nonlinear Mathematics, 31 Jan 2014.

·         Invited seminar: University of Leeds, 2 Dec 2013.

·         Invited speaker at Royal Irish Academy Dublin Talks event, Smock Alley Theatre, 18 Nov 2013.

·         Keynote speaker at Contagion ’13: Modelling of Disease Contagion Processes satellite meeting, European Conference on Complex Systems, Barcelona 18 Sep 2013.

·         Talk at the Collective Contagion satellite workshop, European Conference on Complex Systems, Barcelona 19 Sep 2013.

·         Invited speaker at the Irish Mathematical Society Annual Meeting, Maynooth, 26 Aug 2013.

·         Co-organiser (with Mason Porter) of “Cascades on Networks” minisymposium, SIAM Conference on Applications of Dynamical Systems, Snowbird Utah, 23 May 2013.


Research areas and selected publications


·         Stochastic models of popularity on networks

We are developing models for the diffusion of “memes” or choices among multiple items, in the context of online social networks such as Facebook and Twitter.

·         Gleeson JP, Ward JA, O’Sullivan KP, Lee WT, Competition-induced criticality in a model of meme popularity, Phys. Rev. Lett. 112, 048701 (2014) ; arXiv:1305.4328. This paper was selected for a Synopsis article in APS Physics.

·         Gleeson JP, Cellai D, Onnela J-P, Porter MA, Reed-Tsochas F, A simple generative model of collective online behaviour, arXiv:1305.7440

·         Complex networks: dynamics and structural models

We have developed methods for analytically calculating the expected size of cascades on random networks, and on networks with clustering (transitivity) and modular structures [11-14]. Recently we extended these methods to a general class of binary-state dynamics [3-8]. We have also investigated why mean-field theory often works well, even on highly-clustered networks [9,10],  and we are interested in generalizing results to multiplex networks [1,2].

1.      Cellai D, Lopez E, Zhou J, Gleeson JP, Bianconi G, Percolation in multiplex networks with overlap, Phys. Rev. E, 88, 052811 (2013); arXiv:1307.6359

2.      Kivelä M, Arenas A, Barthelemy M, Gleeson JP, Moreno Y, Porter MA, Multilayer networks, arXiv:1309:7233

3.      Gleeson JP, Binary-state dynamics on complex networks: pair approximation and beyond, Phys. Rev. X, 3, 021004 (2013) (open access). Octave/Matlab solvers for the differential equations in this paper are available for download from here.

4.      Melnik S, Ward JA, Gleeson JP, Porter MA, Multi-stage complex contagion, Chaos, 23, 013124 (2013);  arXiv:1111.1596

5.      Cellai D, Lawlor A, Dawson KA, Gleeson JP, Critical phenomena in heterogeneous k-core percolation, Phys. Rev. E, 87, 022134 (2013); arXiv:1209.2928

6.      Durrett R, Gleeson JP, Lloyd AL, Mucha PJ, Shi F, Sivakoff D, Socolar JES and Varghese C, Graph fission in an evolving voter model, Proc. Natl. Acad. Sci. USA, 109, 3682 (2012) (open access).

7.      Gleeson JP, High-accuracy approximation of binary-state dynamics on networks, Phys. Rev. Letters, 107, 068701 (2011); extended version at arXiv:1104.1537

8.      Cellai D, Lawlor A, Dawson KA, Gleeson JP, Tricritical point in heterogeneous k-core percolation, Phys. Rev. Letters, 107, 175703 (2011); arXiv:1106.1565

9.      Gleeson JP, Melnik S, Ward J, Porter MA, Mucha PJ, Accuracy of mean-field theory for dynamics on real-world networks, Phys. Rev. E, 85, 026106 (2012); arXiv:1011.3710

10.  Melnik S, Hackett A, Porter MA, Mucha PJ, Gleeson JP, The unreasonable effectiveness of tree-based theory for networks with clustering, Phys. Rev. E, 83, 036112 (2011); arXiv:1001.1439

11.  Melnik S, Porter MA, Mucha PJ, Gleeson JP, Dynamics on modular networks with heterogeneous correlations, arXiv:1207.1809 (2012)

12.  Hackett A and Gleeson JP, Cascades on clique-based graphs, Phys. Rev. E,87, 062801 (2013); arXiv: 1206.3075

13.  Gleeson JP, Bond percolation on a class of clustered random networks, Phys. Rev. E, 80, 036107 (2009), arXiv:0904.4292

14.  Gleeson JP, Cascades on correlated and modular random networks, Phys. Rev. E, 77, 046117 (2008); [PDF]


·         Systemic risk models for contagion in banking networks

We examine how the topology of banking networks can lead to system-wide contagion, using a variety of models for bank default.

15.  Hurd TR and Gleeson JP, On Watts’ cascade model with random link weights, Journal of Complex Networks, 1, 25-43 (2013); arXiv:1211.5708

16.  Hurd TR and Gleeson JP, A framework for analyzing contagion in banking networks, submitted; arXiv:1110.4312

17.  Gleeson JP, Hurd TR, Melnik S, Hackett A, Systemic risk in banking networks without Monte Carlo simulation, in Advances in Network Analysis and its Applications, E. Kranakis ed., pp27-56, Springer (2012) PDF.


·         Mathematical modelling

Mathematical modelling of stochastic effects, in collaboration with engineers and applied scientists, e.g., noise in electronic oscillators [18,19], mixing, sorting and diffusion in microfluidic  devices [20-23].

18.  O’Doherty F and Gleeson JP, Phase diffusion coefficient for oscillators perturbed by colored noise, IEEE Trans. Circuits and Systems II, 54, 435-439 (2007). [PDF]

19.  Gleeson JP and O’Doherty F, Non-Lorentzian spectral lineshapes near a Hopf bifurcation, SIAM J. Appl. Math., 66, 1669-1688 (2006) [PDF]

20.  Lanyon YH et al., Fabrication of nanopore array electrodes by focused ion beam milling, Anal. Chem., 79, 3048 (2007) [PDF]

21.  Gleeson JP, Sancho JM, Lacasta AM, and Lindenberg K, Analytical approach to sorting in periodic and random potentials, Phys. Rev. E, 73, 041102 (2006) [PDF]

22.  Gleeson JP, Transient micromixing: Examples of laminar and chaotic stirring, Phys. Fluids, 17, 100614 (2005) [PDF]

23.  Gleeson JP, Roche OM, West J, and Gelb A, Modelling annular micromixers, SIAM J. Appl. Math., 64, 1294-1310 (2004) [PDF]




Complete list of publications

Stochastic Dynamics and Complex Systems (SDCS) homepage

MACSI homepage

Mathematics and Statistics homepage