Nonlinear dynamics & stochastic processes in cybersecurity applications

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Ryan, Pierce
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University College Cork
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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.
Cybersecurity , Nonlinear dynamics , Stochastic processes , Dynamical systems , Time delay
Ryan, P. 2023. Nonlinear dynamics & stochastic processes in cybersecurity applications. PhD Thesis, University College Cork.
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