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A list of all the posts and pages found on the site. For you robots out there is an XML version available for digesting as well.
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Biography
Lecturer in Applied Mathematics at Technological University Dublin. Research interests include: Nonlinear dynamics, Data Modelling, Internet Systems
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Posts
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portfolio
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publications
Border-collision bifurcations in a driven time-delay system
Published in Chaos: An Interdisciplinary Journal of Nonlinear Science, 2020
We show that a simple piecewise-linear system with time delay and periodic forcing gives rise to a rich bifurcation structure of torus bifurcations and Arnold tongues, as well as multistability across a significant portion of the parameter space. The simplicity of our model enables us to study the dynamical features analytically. Specifically, these features are explained in terms of border collision bifurcations of an associated Poincaré map. Given that time delay and periodic forcing are common ingredients in mathematical models, this analysis provides widely applicable insight.
Recommended citation: Border-collision bifurcations in a driven time-delay system, Chaos: An Interdisciplinary Journal of Nonlinear Science, 30(2):023121, 2020. https://doi.org/10.1063/1.5119982
Dynamics of Targeted Ransomware Negotiation
Published in IEEE Access, 2022
In this paper, we consider how the development of targeted ransomware has affected the dynamics of ransomware negotiations to better understand how to respond to ransomware attacks. We construct a model of ransomware negotiations as an asymmetric non-cooperative two-player game. In particular, our model considers the investments that a malicious actor must make in order to conduct a successful targeted ransomware attack. We demonstrate how imperfect information is a crucial feature for replicating observed real-world behaviour. Furthermore, we present optimal strategies for both the malicious actor and the target, and demonstrate how imperfect information results in a non-trivial optimal strategy for the malicious actor.
Recommended citation: P. Ryan, J. Fokker, S. Healy and A. Amann, Dynamics of targeted ransomware negotiation, IEEE Access, 10:3283632844, 2022 https://ieeexplore.ieee.org/document/9738625
Nonlinear dynamics & stochastic processes in cybersecurity applications
Published in University College Cork, 2023
The Internet is an extremely complex system which has a significant impact on the world we live in. In this thesis, we formalise Internet-based problems as mathematical models to better understand their dynamics. Modelling these problems requires dynamical features such as time delay, periodic forcing, switching and stochasticity. We study several dynamical systems which employ a combination of these features from Internet applications, including targeted ransomware, data networks, and signal processing. We also study a climate science system which shares features with the signal processing system and exhibits similar dynamics. Stochasticity is found to be critical in the modelling of the negotiations involved in targeted ransomware, while time delay is a crucial feature in the modelling of data networks. The signal processing and climate science systems give rise to extremely rich dynamics, which we are able to study analytically due to the presence of switching. This yields further insights into related smooth systems.
Recommended citation: Pierce Ryan, "Nonlinear dynamics & stochastic processes in cybersecurity applications", University College Cork, 2023. https://cora.ucc.ie/items/d836b8ab-70b3-479b-a951-359480721c8a
Dynamics of a time-delayed relay system
Published in Physical Review E, 2024
We study the dynamics of a piecewise-linear second-order delay differential equation that is representative of feedback systems with relays (switches) that actuate after a fixed delay. The system under study exhibits strong multirhythmicity, the coexistence of many stable periodic solutions for the same values of the parameters. We present a detailed study of these periodic solutions and their bifurcations. Starting from an integro-differential model, we show how to reduce the system to a set of finite-dimensional maps. We then demonstrate that the parameter regions of existence of periodic solutions can be understood in terms of discontinuity induced bifurcations and their stability is determined by smooth bifurcations. Using this technique we are able to show that slowly oscillating solutions are always stable if they exist. We also demonstrate the coexistence of stable periodic solutions with quasiperiodic solutions.
Recommended citation: Lucas Illing, Pierce Ryan, and Andreas Amann. Dynamics of a time-delayed relay system. Phys. Rev. E , 109:014223, 2024. https://journals.aps.org/pre/abstract/10.1103/PhysRevE.109.014223
talks
Talk: Border-collision bifurcations in a driven time-delay system
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Oral presentation on the paper of the same name given as part of the UCC School of Mathematical Sciences seminar series.
Conference talk: Border-collision bifurcations in a driven time-delay system
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Oral presentation on the paper of the same name presented at the online conference Dynamic Days Digital 2020, which originally had been Dynamic Days Europe 2020 before being forced online by the COVID-19 pandemic.
Poster: Dynamics of targeted ransomware negotiation
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Poster presentation of the paper of the same name at the Dynamic Days Europe 2022 conference.
Conference talk: Symbolic dynamics of a driven time-delay system
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Oral presentation covering a previously published paper, taking into account more recent study in the field. Link to slides
Conference talk: Dynamics of relay systems with bandpass filtered feedback
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Oral presentation of a preprint, written in collaboration with Dr. Andreas Amann and Dr. Lucas Illing. Link to slides
teaching
AM3051 Vector & Tensor Methods
Lecturer in Applied Mathematics, University College Cork, School of Mathematical Sciences, 2020
From 2020 to 2022, I had sole responsibility for the teaching, examination, and administration of this module, taken by third year Mathematical Sciences students. This module introduces the tensor algebra required for advanced partial differential equations modules, and covers topics such as solving the Laplace equation in spherical and cylindrical coordinates.
AM1052 Introduction to Mechanics
Lecturer in Applied Mathematics, University College Cork, School of Mathematical Sciences, 2022
I had sole responsibility for the teaching, examination, and administration of this module, taken by over 100 first year Mathematical Sciences students. The goal of this module is to provide an understanding of the fundamentals of vector algebra through the application of Newtonian mechanics. I supervised 4 undergraduate tutors who gave tutorials for this module.
AM3063 Partial Differential Equations with Applications
Lecturer in Applied Mathematics, University College Cork, School of Mathematical Sciences, 2022
I had sole responsibility for the teaching, examination, and administration of this module, taken by third year and fourth year undergraduate students and postgraduate students. The core goal of this module is to teach the fundamentals of vector algebra through the application of Newtonian mechanics. This module covers methods of solving first and second-order PDEs, including classical examples such as the wave equation.
AM4065 Network Science: Theory and Applications
Lecturer in Applied Mathematics, University College Cork, School of Mathematical Sciences, 2022
I had sole responsibility for the teaching, examination, and administration of this module, taken by fourth year undergraduate students and postgraduate students. This module covers topics in network science and graph theory, such as structural properties of social networks.
ST1023 Introduction to Business Statistics
Postdoctoral researcher in Applied Mathematics, University College Cork, School of Mathematical Sciences, 2023
I had sole responsibility for the teaching, examination, and administration of this module, taken by over 480 first year Business students. The goal of this module is to provide an understanding of the basic methods of business statistics. I supervise 4 undergraduate tutors who give tutorials for this module.