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chair: Anna von der Heydt
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09:00 - 09:30
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Wei Lin
(Fudan University, Shanghai)
Predicting and modulating complex dynamics using data-driven and machine learning techniques
In the era of the data science, model-free techniques are developed overwhelmingly. When the experimentally-collected data are generated by dynamical systems, the missions of reconstruction, prediction, and modulation only based on these data are highly anticipated to be achieved for these systems. Here, we introduce several directions of progresses made by our research group in developing the model-free techniques using machine learning techniques and dynamical systems theory. We use representative systems of physical or/and biological significance to demonstrate the developed techniques. We hope that all the methods can shed a light on deciphering and controlling the hidden dynamics that dominate the evolutions of any systems in real-world.
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09:30 - 10:00
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Klaus Lehnertz
(University Hospital Bonn)
Critical transitions in the human brain: early warning signals and prediction of epileptic seizures
The human brain is an open, dissipative, and adaptive nonstationary dynamical system composed of a large number of interacting subsystems. Its complicated spatial–temporal dynamics is still poorly understood. Epilepsy is a malfunction of the brain that affects about 50 million people worldwide.
Epileptic seizures are the cardinal symptom of the disease and often appear as a transformation of otherwise normal brain dynamics.
The exact mechanisms underlying seizure generation are still as uncertain as are mechanisms underlying seizure spreading and termination.
Identifying early warning signals of seizures from brain dynamics could drastically improve therapeutic possibilities and thus, the quality of life of people with epilepsy.
Methods from nonlinear dynamics, statistical physics, synchronization and network theory are capable of identifying seizure precursors from EEG recordings in a large number of people with epilepsy and with high sensitivity and specificity.
In this talk, I will provide a brief overview of the current status of the field, will highlight shortcomings of recent approaches as well as unsovled issues, and will discuss possible research directions that may help to find better solutions.
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10:00 - 10:20
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Tamás Kovács
(Eötvös Loránd University)
Stellar orbits beyond the adiabatic limit
Motion of stars is usually considered in time independent galactic potential. However, for various circumstances (e.g. encounters between the individual stars; stars of galaxies and globular clusters lose substantial quantities of mass) one have to take into account potential variations that are slow (or adiabatic) compared to a typical orbital frequency. In this case the action variables of stars are constant during such adiabatic changes of the potential. For this reason actions are often called adiabatic invariants.
The nature of the problem posed by a time-varying potential depends on the speed with which the potential evolves. In slowly evolving potentials, angle-action variables enable us to predict how a stellar system will respond to changes in the gravitational field that confines it. We seek in our research a novel approach to describe the dynamics beyond the adiabatic limit, i.e. when the change of potential is comparable to the characteristic time scale of the problem. To our knowledge this is the first attempt to use contemporary results of nonautonomous Hamiltonian dynamics in celestial mechanics. We hope that this idea will enable us to explore the peculiar nature of stellar dynamics subjected to external forces.
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10:20 - 10:40
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Reyk Börner
(University of Reading)
Melancholia state of the Atlantic ocean circulation in an intermediate-complexity climate model
The Atlantic Meridional Overturning Circulation (AMOC) is believed to possess two stable flow regimes, thus qualifying as a proposed tipping element in the Earth system. Abrupt climate changes in paleo records are often associated with shifts between different AMOC flow patterns. To better understand the mechanisms and probability of such transitions, it is important to understand their transition pathway in the state space of climate models. Specifically, in weakly perturbed dynamical systems, it is expected that sample transitions will cross from one to another basin of attraction via special regions on the basin boundary, termed Melancholia states. Here we implement an edge-tracking algorithm in PlaSim-LSG, a global climate model of intermediate complexity, to identify a Melancholia state between the vigorous and collapsed states of the AMOC. We discuss the properties of such a state, its role for critical transitions of the AMOC, and its dependence on time-dependent forcing. Knowing what lies in between the competing metastable states could help elucidate the risk and most likely scenario of potential future AMOC tipping.
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10:40 - 11:20
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coffee break
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chair: Klaus Lehnertz
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11:20 - 11:50
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Henk Dijkstra
(Utrecht University)
Tipping of the AMOC in a Hierarchy of Models
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11:50 - 12:10
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Syamal Kumar Dana
(Jadavpur University)
Tipping in an ecological model under multiple impulsive forces
Syamal Kumar Dana
Centre for Mathematical Biology and Ecology, Department of Mathematics, Jadavpur University, Kolkata 700032, India
Abstract:
We report tipping in an insect outbreak model near two saddle-node bifurcation points of the model system. The model defines outbreak of budworm population from a desirable low population state against the carrying capacity. If the carrying capacity is varied at a linear rate, the system does not show sharp transitions immediately at the bifurcation points but tips to the alternate states after a lapse of time. This delay in tipping decreases with faster rate of change of the carrying capacity. We check the impact of a shock (external effect) modelled by a triangular shape impulse that slowly varies the carrying capacity at a constant rate, however, withdrawn at an identical or different constant rate. The tipping occurs in such cases but shows a dependence on the falling and rising rates of the impulse that influences the carrying capacity. We identify the rate of rising and falling in a phase diagram that provides information when a tipping may occur. An interplay of the dissipation rate of the system and the rate parameter decides the occurrence of tipping. In case of insufficient strength of a single impulse that may fail to induce any tipping to the desirable low population state from a large population or an outbreak state, a second impulse is applied, but weaker in strength compared to the first one and it is able to induce a tipping that prevents an insect outbreak. Therefore, in a situation of multiple shocks or impulses applied on the carrying capacity, tipping may occur as a consequence of past environmental changes. We explain the scenarios with numerical experiments and using the dynamical change in the potential function of the system.
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12:10 - 12:30
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Camille Hankel
(Harvard University)
An Approach for Projecting the Timing of Abrupt Winter Arctic Sea Ice Loss
Abrupt and irreversible winter Arctic sea ice loss may occur under anthropogenic warming due to the disappearance of a sea ice equilibrium at a threshold value of CO$_2$, commonly referred to as a tipping point. Previous work has been unable to conclusively identify whether a tipping point in winter Arctic sea ice exists because fully coupled climate models are too computationally expensive to run to equilibrium for many CO2 values. Here, we explore the non-autonomous behavior of sea ice under realistic rates of CO2 increase to demonstrate for the first time how a few time-dependent CO2 experiments can be used to predict the existence and timing of sea ice tipping points without running the model to steady state. This work highlights the inefficacy of using a single experiment with slow-changing CO2 to discover changes in the sea-ice steady state and provides a novel alternate method that can be developed for the identification of tipping points in realistic climate models.
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12:30 - 13:00
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Niklas Boers
(TU Munich)
Climate Tipping Points - Empirical evidence, uncertainties, and future risks
Several Earth system components have been suggested to exhibit alternative stable states, and for some paleoclimate evidence of abrupt transitions indeed indicates abrupt shifts between states in past climates. Well-known examples include the polar ice sheets, the Atlantic Meridional Overturning Circulation, or the Amazon rainforest. I will present some recent results on the stability of these systems from empirical evidence and model simulations, focussing on the application of concepts from dynamical systems theory.
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13:00 - 15:00
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lunch break
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chair: Henk Dijkstra
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15:00 - 15:30
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Stefano Pierini
(Universita degli Studi di Napoli Parthenope)
The Pullback Attractors of an Excitable Low-Order Ocean Model with Periodic, Aperiodic and Monotonically Drifting Forcing
An excitable low-order quasigeostrophic model [1] captures key features of intrinsic low-frequency variability of the oceans’ wind-driven circulation. This double-gyre model is used as a prototype of an excitable nonlinear dynamical system with time-dependent forcing to explore basic features of climate change in the presence of natural variability. The present studies rely on the theoretical framework of nonautonomous dynamical systems and of their pullback attractors (PBAs), namely the time-dependent invariant sets that attract all trajectories initialized in the remote past. Ensemble simulations help us explore these PBAs.
In an excitable dynamical system, a relaxation oscillation connects a basic state to an unstable excited state, from which spontaneous returns to the original state occur. Such back-and-forth oscillations are self-sustained in a certain parameter range of the autonomous system, and they can be excited by a suitable external time-dependent forcing outside this range.
In this presentation, by using model [1] in its excitable state, we discuss: (i) the effect of a periodic forcing on synchronization scenarios and on the onset of chaos in an otherwise non-chaotic system [2,3]; (ii) the effect of an aperiodic forcing mimicking a time dependence dominated by interdecadal and high-frequency variability [4,5]; (iii) the tipping points due to parameter drift in the presence of small periodic perturbations [6]. The latter situation can be thought of as the seasonal-to-interannual variability in the wind stress, while the monotonically increasing component stands for the effect of reduction in the midlatitude winds due to anthropogenic warming.
References: [1] Pierini S., 2011. J. Phys. Oceanogr. 41, 1585-1604. [2] Pierini S., 2014. J. Phys. Oceanogr. 441, 3245-3254. [3] Pierini S., Chekroun M.D., Ghil M., 2018. Nonlin. Processes Geophys. 25, 671-692. [4] Pierini S., Ghil M., Chekroun M.D., 2016. J. Climate 29, 4185-4202. [5] Pierini S., 2020. J. Stat. Phys. 179, 1475-1495. [6] Pierini S., Ghil M., 2021. Sci. Rep. 11, 11126
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15:30 - 16:00
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Tamás Tél
(Eötvös Loránd University)
How does a chaotic dynamical system undergo its own climate change?
Any dynamical system subjected to monotonous parameter drift can be considered to undergo its own climate change if the rate of the parameter change is not adiabatically slow. Such a situation calls for ensemble simulations, proposed in chaos theory with the appearance of snapshot attractors, as early as 1990. In systems exhibiting trends, basic methods of standard chaos theory are not applicable: the efficient tool of periodic orbit expansion cannot be used since periodic orbits do not exist. Furthermore, long-time limits are ill-defined since the system might become qualitatively different from the original one even after short times. The talk deals with the question of how to identify chaos in such systems. From the point of view of phase space structures, we argue that stable and unstable foliations are easy to generate numerically, without relying on the existence of hyperbolic periodic orbits. Chaos originates from a Smale horseshoe-like pattern of the foliations, the transverse intersections of which indicate a chaotic set changing in time. We discuss in which sense such a process is related to transient chaos and time-dependent chaotic saddles. In dissipative cases, the unstable foliation is found to be part of the chaotic snapshot attractor, while the stable one turns out to be related to the basin of attraction of the time-dependent chaos. Concerning a quantitative characterization, the so-called ensemble-averaged pairwise distance is shown to provide a generalization of the concept of Lyapunov exponents, since the slope of this function can be interpreted as an instantaneous Lyapunov exponent. This is a tool by means of which a strengthening, weaking, or even disappearance of chaos can be investigated.
D. Jánosi, T. Tél: Characterizing chaos in systems subjected to parameter drift, Phys. Rev. E 105, L062202 (2022)
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16:00 - 16:20
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Paul Ritchie
(University of Exeter)
Rate-induced tipping in natural and human systems
Over the last two decades, tipping points have become a hot topic due to the devastating consequences that they may have on natural and human systems. Tipping points are typically associated with a system bifurcation when external forcing crosses a critical level, causing an abrupt transition to an alternative, and often less desirable, state. However, the rate of change in forcing is arguably of even greater relevance in the human-dominated anthropocene, but is rarely examined as a potential sole mechanism for tipping points. Thus, I will introduce the related phenomenon of rate-induced tipping: an instability that occurs when external forcing varies across some critical rate, usually without crossing any bifurcations. First, I will explain when to expect rate-induced tipping. Then, using illustrating examples of differing complexity I will highlight universal and generic properties of rate-induced tipping in a range of natural and human systems.
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16:20 - 16:40
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Subhendu Bhandary
(University of Zurich)
Rising Temperature Drives Tipping Points in Mutualistic Network
The effect of climate warming on species' physiological parameters, including growth rate, mortality rate, and handling time, is well established from empirical data. However, with an alarming rise in global temperature more than ever, predicting the interactive influence of these changes on mutualistic communities remains uncertain. Using 139 real plant–pollinator networks sampled across the globe and a modeling approach, we study the impact of species’ individual thermal responses on mutualistic communities. We show that at low mutualistic strength plant–pollinator networks are at potential risk of rapid transitions at higher temperatures. Evidently, generalist species play a critical role in guiding tipping points in mutualistic networks. Further, we derive stability criteria for the networks in a range of temperatures using a two-dimensional reduced model. We identify network structures that can ascertain the delay of a community collapse. Until the end of this century, on account of increasing climate warming many real mutualistic networks are likely to be under the threat of sudden collapse, and we frame strategies to mitigate this. Together, our results indicate that knowing individual species' thermal responses and network structure can improve predictions for communities facing rapid transitions.
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16:40 - 17:00
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coffee break
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17:00 - 18:00
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Poster introduction (part 2 - even poster numbers)
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18:00 - 19:00
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dinner
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19:00
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Poster session II (with focus on even poster numbers)
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