TL;DR
The main focus of the presentation will be the impact of time delays on the stability and dynamics of stationary solutions and the possibility of periodic solutions and the role of delay-induced oscillations in biological models.
Temporal oscillations arise naturally in biological systems with feedback loops or explicit delays. When incorporating spatial effects, the travel times of propagating signals can also generate intrinsic delays, and this behaviour is complicated further in the presence of spatial heterogeneity. In this work, we investi...
The role of time delays in a mathematical model describing the dynamics of TGF-β in epithelial–mesenchymal transition (EMT) and mesenchymal–epithelial transition (MET) in cancer cells is investigated and the influence of the delay representation on the model dynamics is further investigated numerically.
Ordinary differential equations are commonly used throughout the sciences to build mechanistic models of time-dependent processes. Often, such models are Markov models describing the time-evolution of different interconnected"states". When these models have no"sources"or"sinks", they naturally conserve the total popula...
Topological signals are dynamical variables supported on higher-order structures such as simplicial or cell complexes. In this work, we investigate the impact of time-delayed interactions on the emergence of global synchronization of topological oscillators, with application to the Stuart-Landau system. We first examin...
Financial risk dynamics often exhibit irregular fluctuations that are well described by nonlinear models with complex behavior. Motivated by the suitability of discrete-time representations for financial phenomena, this paper develops and studies a discrete-time financial risk evolution model obtained by applying the f...
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