CDSANAB · Complex Dynamics and Strange Attractors through Non-Autonomous Bifurcations
Horizon 2020 — Marie Skłodowska-Curie Actions
- Duration
- 2018-03-01 → 2020-07-31
- EU contribution
- €183,455
- Participants
- 1
- Scheme
- MSCA-IF-EF-ST
Lines connect the coordinator with its partners.
Results in brief
Complex Dynamics and Strange Attractors through Non-Autonomous Bifurcations
An autonomous dynamical system is defined by an evolution law which is constant over time and governs the change of a given system along the progression of time. While much of the theory building with regards to dynamical systems takes place in this autonomous setting, practical applications ask for a better understanding of non-autonomous systems, as real-world models—be it in ecology, climatology or other sciences—typically include external forces. This project accommodated comprehensive rigorous analytical investigations as well as application-oriented research shedding light on the question as to how complex dynamical behaviour—as is visible in the succession of ice ages or other seemingly unpredictable real-world processes—arises. A key notion in this context are so-called bifurcations. These are drastic changes in a system’s behaviour due to minor variations of some parameter(s) of the system. Despite their ubiquity, the prediction of such bifurcations so far simply applied tools whose applicability in a non-autonomous context was hardly investigated prior to this project. Among these tools, the most prominent is to measure so-called recovery rates which indicate how fast a system returns to its equilibrium after having been slightly nudged away from it. The classical theory suggests that when a system approaches a bifurcation, then the time to recover should increase since the system’s stability is less and less ensured the closer we are to a bifurcation.
Data: CORDIS, © European Union
Project objective
This project aims at substantial contributions to the bifurcation theory of non-autonomous dynamical systems. The main research efforts will focus on an analytical investigation of the principles behind the creation of complex dynamical behaviour and strange attractors in the most common kinds of non-autonomous bifurcations: saddle-node and Hopf bifurcations. The project further aims at an interdisciplinary application of the analytical findings to the problem of the predictability of ice ages.The research on non-autonomous saddle-node bifurcations will extend the results of the applicant's PhD. Here, the main strategy is to apply powerful multiscale analysis techniques. Further, it is aimed at providing easily applicable tools for researchers in the life sciences to reliably track complex behaviour near saddle-node bifurcations.The research on the non-autonomous Hopf bifurcation will focus on the creation of chaos. In deterministically driven systems, the analysis will again be based on multiscale analysis techniques. In randomly driven systems, it is aimed at a profound extension of the work by the supervisor and his collaborators on shear-induced chaos.The host institution is not only a leading centre in bifurcation theory and non-autonomous dynamics but also the coordinating institution of the Marie Skłodowska-Curie Innovative Training Network (ITN) CRITICS which addresses critical transitions in complex systems. The interdisciplinary part of the project will be dealt with in collaboration with a partner of this ITN: the Theoretical Climate and Palaeoclimate Dynamics group at the Université catholique de Louvain.The Horizon 2020 key challenges include topics such as food security or climate action. Appropriate measures addressing related issues need to rely on a good understanding of complex systems which are non-autonomous by nature. Thus, profound insights into non-autonomous systems and bifurcations of such systems are of an immense European interest.
Original text from CORDIS.
Participants
- IMPERIAL COLLEGE OF SCIENCE TECHNOLOGY AND MEDICINE · LondonCoordinatorUnited Kingdom
Links
Data: CORDIS, © European Union