Non-autonomous Dynamics in Complex Systems: Theory and Applications to Critical Transitions

According to the goal of this workshop/seminar we brought together scientists from various
disciplines in the natural sciences, such as mathematics, physics, the climate sciences,
neuroscience, ecology, systems biology and network science. Almost all speakers which
have been invited accepted our invitation, so that most of the major players in this field were
present in the workshop. Therefore, this workshop was very attractive for people in the
above areas. Overall, we had at the workshop 90 participants from 21 countries spread over
Europe, Asia, North and South America as well as from Australia. Since this workshop was
planned as an on-site event almost all speakers were in person in Dresden, except for one
speaker from China, who did not get the visa for Germany in time and one speaker from
Israel, who could not leave because of the Gaza conflict. Both invited speakers gave their
talks online. In addition, we had another short-term cancellation due to entry problems at the
border and we filled this slot with another invited speaker, who could not make it to Dresden
on such short notice. All talks were recorded but only available for the participants using their
password for the workshop.

Non-autonomous dynamics as the main theme of the workshop has been presented from a
theoretical point of view featuring new mathematical methodology [A. von der Heydt (The
Netherlands), C.K.R.T. Jones (USA), M. Rasmussen (UK), S. Wieczorek (Ireland)], and
different applications in climate dynamics [T. Tél, Hungary], ecology [E. Meron (Israel), P.
Dutta (India)], neuroscience [K. Lehnertz (Germany)], medical science [L. Chen (China)],
machine learning [P. Tino (UK), Juan-Pablo Ortega (Singapore)], socio-ecological systems
[S. Roman (UK)] and astrophysics [T. Kovács (Hungary)]. Already this list highlights the
interdisciplinarity of the event. Of particular interest for many applications were rate-induced
transitions between the different stable states, a typical bifurcation in non-autonomous
systems also called a tipping point. These bifurcations are caused by changes in the internal
parameters of the system, changes in the forcing leading to a transition from one stable state
to another when the rate of change is larger than a critical rate. Such transitions have been
presented in several applications like the changes in the Atlantic overturning circulation [P.
Ditlevsen (Denmark), H. Dijkstra (The Netherlands)], the melting of ice sheets [M. Montoya
(Spain), or changes in ecosystems [M. Silber (USA)] as a response to climate change. But
also new theoretical ideas such as basin instabilities, the combination of rate-induced and
noise-induced transitions as well as topological instabilities have been presented [G. Charó
(Argentina)]. Besides theoretical investigations based on model systems, new approaches to
identifying critical transitions from time series [N. Boers (Germany)] have been discussed.
Overall, 22 invited talks and 23 contributed talks demonstrated the state-of-the-art in the field
of non-autonomous dynamics in complex systems and facilitated very lively discussions
leading to the intended cross-fertilization between the different fields.

Many of the participants were early career researchers. Therefore, we included 2 poster
sessions, each one in the evening as an “open-ended” event after a short two-minute-
presentation of each poster by its presenter in the afternoon. The broad spectrum of topics in
the talks was also reflected in these two very busy poster sessions where early career
researchers presented their results for an open discussion. All the posters were on a very
high scientific level so that the poster judges, P. Ditlevsen (Denmark), C.K.R.T. Jones
(USA), S. Pierini (Italy), M. Rasmussen (UK) and M. Silber (USA), had a hard time to select
the very best ones for the 3 poster prices.

As a result of this workshop, we expect that several joint papers with different participants of
the workshop will appear in the future. The organizers have arranged for a Focus Issue
dedicated to this workshop in the international peer-reviewed journal CHAOS: An
Interdisciplinary Journal of Nonlinear Science, with about 40 invited papers. This Focus
Issue has already been advertised on the journal’s website,
publishing.aip.org/publications/journals/special-topics/chaos/nonautonomous-
dynamical-systems-theory-methods-and-applications/ and it will appear, we hope and
expect, in early 2025.

Overall, this workshop was a very successful event, bringing together scientists from various
disciplines, which usually would not meet in their different disciplinary conferences. The
organizers got a lot of positive feedback afterwards, encouraging us to organize another
event of similar format at some later time. Since this field of research is still in its infancy but
rapidly developing, organizing such a follow-up event in the coming years is sound advice.

One week before and after the workshop we organized a seminar, which had a school-like
character with lectures given by C.R.K.T. Jones (USA), K. Lehnertz (Germany), E. Meron
(Israel), M. Rasmussen (UK), D. Sciamarella (Argentina) and the three organizers. In
addition, three short courses including hands-on parts were presented by I. Longo (UK) on
“Critical transitions in non-autonomous systems”, M. Ghil and D. Ohara on “Singular
Spectrum Analysis” and G. Datseris (UK) on “Programing Language Julia and its Application
in Dynamical System Theory”. This program attracted many early career researchers. Thus,
we had to make a very restrictive selection of the participants, since we had 44 applicants for
only 25 places, including the places for the lecturers. We followed the rule that from each
working group we only accepted one student or postdoc. To solve the problem which
student/postdoc to choose from several applications in the same group, we communicated
with the supervisors of the applicants. This way a group of 20 students coming from 17
distinct universities and scientific institutes was selected, supplemented by 4 local students,
3 from the Max-Planck-Institute for Physics of Complex Systems and 1 from the Max-Planck-
Institute for Animal Behavior: overall, just 15 PhD students and 9 postdocs from 9 countries.