Early Stage Researchers
I am a PhD student at Imperial College London under the supervision of Prof. Dmitry Turaev and Prof. Jeroen Lamb. My research is mainly focused on the study of dynamics of a system of differential equations in presence of “homoclinic to homoclinic” (an orbit which is alpha-limit and omega-limit to a homoclinic loop) or simply “super-homoclinic” orbits. A rich dynamics might arise by these orbits and I try to investigate this dynamical behavior in my PhD project.
I am currently enrolled as a PhD student at the Institute of Atmospheric and Marine Resarch Utrecht (IMAU), at Utrecht University, under the supervision of Prof. Henk Dijkstra. My research is focused on the stochastic modelling of the oceans. The Atlantic Ocean circulation, in particular its Meridional Overturning Circulation (MOC), is sensitive to freshwater anomalies. A tipping point may exist such that the present-day MOC will collapse if the northern North Atlantic freshwater forcing is gradually increased. The aim of my project is to determine the probability of transitions of the Meridional Overturning Circulation (MOC) in a hierarchy of stochastic ocean-climate models. I hold a MSc in Theoretical Physics from Sapienza University in Rome (Italy).
Currently I am a PhD student at Imperial College London (UK) under the supervision of Sebastian van Strien and Martin Rasmussen. In my PhD project I examine bifurcations in dynamical systems that are defined by stochastic approximation algorithms, a type of random non-autonomous non-invertible dynamical systems. Although such systems have been studied in the past, not much attention has been payed to bifurcations therein. The goal is to identify and describe possible bifurcations and the circumstances under which they occur in a mathematically rigorous way. I am holding BSc and MSc degrees in Mathematics from Friedrich-Alexander University of Erlangen-Nuremberg (Germany).
The previous glacial period featured numerous abrupt climatic changes. In particular, a series of rapid warming events have been observed in Greenland ice cores, where temperatures rose by 10-15 K within few decades, followed by a more gradual cooling before temperatures dropped back to full glacial conditions. These so-called Dansgaard-Oeschger (DO) events remain elusive in realistic, fully coupled climate models and their dynamical origin is unknown. In my thesis with Peter Ditlevsen at Københavns Universitet, I combine time series analysis, inverse modeling and statistical model comparison to establish which dynamical paradigm is most likely at work in the observed climate changes. Furthermore, these dynamical paradigms have to be derived from physical considerations and the possibility of early warning has to be explored.
I am currently enrolled as a PhD student at “Universidad de Valladolid” (Spain) under the supervision of Prof. Rafael Obaya and Prof. Sylvia Novo. My research is mainly focused on the study of non-autonomous ordinary and functional differential equations whose vector fields are of Carathèodory type. The aim is to provide a mid-point analysis between the deterministic and smooth dynamical systems and Random Dynamical Systems Theory. My research interests also include problems in non-autonomous Bifurcation Theory and applications to Science and Engineering. I have a MSc and a BA in Mathematics achieved at “Università del Salento” (Italy).
M. Usman Mirza
Usman’s research interest lies in analysing resilience and critical transitions in complex systems related to society, environment and the economy. Currently Usman is a PhD candidate and researcher, supervised by Marten Scheffer and Egbert Van Nes at Wageningen University and Research Centre in the Netherlands. Previously, Usman was based at a think tank in Pakistan – LEAD Pakistan – leading their Water Programme. His work involved policy relevant research on a broad range of aspects including water pricing, groundwater management, climatic impacts and hydro-diplomacy in transboundary water. Usman has a MS in Public Policy from Carnegie Mellon University (CMU), US and a BS in Economics from Lahore University of Management Sciences (LUMS), Pakistan.
I am a PhD student at TU Dresden, supervised by Dr. Kathrin Padberg-Gehle. I have a MSc in Applied Mathematics and Scientific Computing at Universite Gaston Berger de Saint-Louis in Senegal and a postgraduate diploma in Mathematics at the International Center for Theoretical Physics (ICTP) at Trieste, Italy. I aim at developing a novel methodology for identifying and predicting sudden changes in flow patterns based on transfer operator techniques and finite-time bifurcation theory.
Ice ages are examples of phenomena that occur abruptly, perhaps as critical transitions. Under the assumption that the global ice variability in Earth’s climate on long time scales can be effectively described by a dynamical system with few variables, one can try to answer questions such as “What is the dominant mechanism causing the pattern and duration of ice age cycles?” with dynamical systems theory. If one includes radiation from the sun and unresolved processes in Earth’s climate, models become non-autonomous and stochastic, which widens the range of possible system behaviour. Broad questions in my project are “What caused the change in duration of ice ages around one million years ago?” and “What role does isolation play for ice age dynamics?”.
My research focuses on model-order reduction techniques for high-dimensional stochastic differential equations modeling complex phenomena in physics, finance and technology. The high dimensionality usually inhibits theoretical or computational understanding of the underlying system. Therefore, appropriate low-dimensional surrogate models are required. The main question currently concerns the error incurred by using reduced-order models. Furthermore, implications for critical transitions and the application to stochastic filtering is of interest. I hold an MSc and BSc in mathematics, both from University of Augsburg.
I am currently completing research regarding delay effects in paleoclimate models under the supervision of Dr. Jan Sieber at the University of Exeter (Exeter, UK). My current project involves incorporating delays into low-order, conceptual models of the Quaternary era and analysing critical transitions through bifurcations of these delayed systems. I have a MSc in Atmosphere-Ocean Dynamics from University of Leeds (Leeds, UK) along with a BA in Mathematics and a BA in Music from Rowan University (NJ, USA). My other research areas of interest are in climate change and dynamics of extreme weather.
I am currently a PhD student at Friedrich-Schiller-Universität Jena (Germany), in the group of Ergodic theory and Dynamical Systems. My research interest at the moment is to investigate and identify early warning signals for Fold bifurcations in randomly and deterministically forced systems in population dynamics under the supervision of Prof. Tobias Oertel-Jäger and Dr. Gabriel Fuhrmann. I hold an Msc in Mathematical modelling from Makerere Unversity and Bsc in Education, Physics/Mathematics (Uganda).
Pablo Rodríguez-Sánchez holds a MSc in theoretical physics by Universidad Complutense de Madrid. He is currently enrolled as PhD student in Wageningen UR, Netherlands. His research is focused on modeling, simulating and studying structural stability of biological systems described by non-linear and stochastic dynamics. In his free time, he participates enthusiastically in various science communication and science teaching projects (like, for example, the science e-magazine naukas.com).
My analysis is concerned with using and extending theory of dynamical systems and bifurcations in financial systems, providing early-warning signals for market bubbles and crashes and determining how we can include in the models as well intrinsically as extrinsically caused bubbles. So far I have worked on a deterministic system of an asset and a bond where one can observe crashes, but I would like to extend it by financially justified stochastic terms and to determine whether I would be able to use tipping points theory to predict sudden stock falls.
I am currently enrolled as a PhD student at Imperial College London, under the supervision of Professor Grigorios Pavliotis. The aim of my project is to develop more efficient and accurate numerical algorithms for analysing and simulating the generalized Langevin equation (GLE), a stochastic differential equation which has recently gained popularity as a more realistic model for several phenomena in different contexts, including anomalous diffusion in biological fluids, microrheology, heat transport within nano-scale devices, and nuclear quantum effects. In climate modeling the GLE arises through the Mori-Zwanzig formalism as the equation describing the coarse-grained reduced-order model of an initially high-order model. The advantage of the GLE over the conventional Langevin equation is that it allows for the incorporation of temporally non-local drag forces through an integration kernel in the diffusion term. This also poses new challenges for both the analytical and numerical treatment of the dynamics described by the equation.
Ke is currently a PhD student in ETH Zurich, supervised by Prof. Didier Sornette. Ke is interested in critical transitions in finance, especially in the search for the formation, mechanisms and characterization of the dynamics during financial market crashes. At the same time, he is also interested in the study of prediction market and trading strategy. Ke has years of hands-on experience in quantitative trading and would like to promote research application in industry and facilitate the cooperation between the two in the future. Ke has a MA in mathematical finance (MAFN) from Columbia University, a double BA in Economics from Peking University, and a BS in mathematics from Beijing Normal University.
Critical transitions or tipping points are widely implemented in complex systems such as economics, climate, biology, and etc., as the analysis of the early-warning signals for unexpected changes of the systems. Generally, three categories of tipping are respectively due to bifurcation, noise fluctuation and changing rate of external conditions. My research focuses on rate-induced tipping to explore the critical level of the varying external conditions, acting as the early-warning predictions, under the supervision of Prof. Wieczorek at University College Cork, Ireland. And I hold a MSc in Mechanical Engineering from EPFL, Switzerland and a B.E. in Mechatronics Engineering from Harbin Institute of Technology, China.
Peter Ashwin (University of Exeter)
Research expertise: Bifurcation theory, Coupled system dynamics, Tipping points _____________________________
Henk Dijkstra (Utrecht University)
Research expertise: Dynamical Systems, Climate Dynamics ______________________________
Peter Ditlevsen (Niels Bohr Institute)
Research expertise: Climate research, Turbulence, Meteorology, Complex systems, Time series analysis and Statistical physics
Jeroen Lamb (Imperial College London)
Research expertise: Local and global bifurcation theory, Dynamics and spatio-temporal symmetry, Aperiodic tilings (Quasicrystals, tiling dynamical systems), Random dynamical systems, Network dynamical systems __________________________ ______________________
Tim Lenton (University of Exeter)
Research expertise: Earth system science, Climate change, Global biogeochemical cycles, Co-evolution of life and the planet, Paleo-climate modelling
Egbert van Nes (Wageningen University)
Research expertise: Theoretical ecology, Ecological models, Critical transitions, Resilience indicators
Tobias Oertel-Jäger (Friedrich-Schiller-Universität Jena)
Research expertise: Ergodic theory and dynamical systems, Low-dimensional dynamics, Non-autonomous bifurcation theory, Fractal attractors
Rafael Obaya (University of Valladolid)
Research expertise: Nonautonomous dynamics, Bifurcation theory, Nonautonomous control theory, Mathematical modelization
Kathrin Padberg-Gehle (Technische Universität Dresden)
Research expertise: Computational dynamics, Numerical ergodic theory, Nonautonomous dynamics, Transport
Martin Rasmussen (Imperial College London)
Research expertise: Nonautonomous dynamical systems, Random dynamical systems, Bifurcation theory
Jan Sieber (University of Exeter)
Research expertise: Nonlinear dynamics, Effects of delays, Tracking of unstable phenomena in experiments
Didier Sornette (ETH Zürich)
Research expertise: Predictability and control of crises and extreme events in complex systems, Financial bubbles and crashes, Earthquake physics and geophysics, Dynamics of social networks and the complex system approach to medicine_______________________________________
Sebastian Wieczorek (University College Cork)
Research expertise: Dynamical Systems, Applied Bifurcation Theory, Nonlinear Science, Tipping Points