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Jürgen Kurths

Publications and source records attributed to Jürgen Kurths.

At least 73 records · Page 4Linked to original sources
arXiv2024

Impact of periodic vaccination in SEIRS seasonal model

We study three different strategies of vaccination in a SEIRS (Susceptible--Exposed--Infected--Recovered--Susceptible) seasonal forced model, which are: ($i$) continuous vaccination; ($ii$) periodic short time localized vaccination and ($iii$) periodic pulsed width campaign. Considering the first strategy, we obtain an expression for the basic reproduction number and infer a minimum vaccination rate necessary to ensure the stability of the disease-free equilibrium (DFE) solution. In the second strategy, the short duration pulses are added to a constant baseline vaccination rate. The pulse is applied according to the seasonal forcing phases. The best outcome is obtained by locating the intensive immunization at inflection of the transmissivity curve. There, a vaccination rate of $44.4\%$ of susceptible individuals is enough to ensure DFE. For the third vaccination proposal, additionally to the amplitude, the pulses have a prolonged time width. We obtain a non-linear relationship between vaccination rates and the duration of the campaign. Our simulations show that the baseline rates, as well as the pulse duration, can substantially improve the vaccination campaign effectiveness. These findings are in agreement with our analytical expression. We show a relationship between the vaccination parameters and the accumulated number of infected individuals, over the years and show the relevance of the immunisation campaign annual reaching for controlling the infection spreading. Regarding the dynamical behaviour of the model, our simulations shows that chaotic and periodic solutions, as well as bi-stable regions, depend on the vaccination parameters range.

physics.bio-ph↗
arXiv2024

Extended generalized recurrence plot quantification of complex circular patterns

The generalized recurrence plot is a modern tool for quantification of complex spatial patterns. Its application spans the analysis of trabecular bone structures, Turing patterns, turbulent spatial plankton patterns, and fractals. Determinism is a central measure in this framework quantifying the level of regularity of spatial structures. We show by basic examples of fully regular patterns of different symmetries that this measure underestimates the orderliness of circular patterns resulting from rotational symmetries. We overcome this crucial problem by checking additional structural elements of the generalized recurrence plot which is demonstrated with the examples. Furthermore, we show the potential of the extended quantity of determinism applying it to more irregular circular patterns which are generated by the complex Ginzburg-Landau-equation and which can be often observed in real spatially extended dynamical systems. So, we are able to reconstruct the main separations of the system's parameter space analyzing single snapshots of the real part only, in contrast to the use of the original quantity. This ability of the proposed method promises also an improved description of other systems with complicated spatio-temporal dynamics typically occurring in fluid dynamics, climatology, biology, ecology, social sciences, etc.

nlin.PS↗
arXiv2024

Regime change detection in irregularly sampled time series

Irregular sampling is a common problem in palaeoclimate studies. We propose a method that provides regularly sampled time series and at the same time a difference filtering of the data. The differences between successive time instances are derived by a transformation costs procedure. A subsequent recurrence analysis is used to investigate regime transitions. This approach is applied on speleothem based palaeoclimate proxy data from the Indonesian-Australian monsoon region. We can clearly identify Heinrich events in the palaeoclimate as characteristic changes in the dynamics.

physics.data-an↗
arXiv2024

Visualizing driving forces of spatially extended systems using the recurrence plot framework

The increasing availability of highly resolved spatio-temporal data leads to new opportunities as well as challenges in many scientific disciplines such as climatology, ecology or epidemiology. This allows more detailed insights into the investigated spatially extended systems. However, this development needs advanced techniques of data analysis which go beyond standard linear tools since the more precise consideration often reveals nonlinear phenomena, for example threshold effects. One of these tools is the recurrence plot approach which has been successfully applied to the description of complex systems. Using this technique's power of visualization, we propose the analysis of the local minima of the underlying distance matrix in order to display driving forces of spatially extended systems. The potential of this novel idea is demonstrated by the analysis of the chlorophyll concentration and the sea surface temperature in the Southern California Bight. We are able not only to confirm the influence of El Niño events on the phytoplankton growth in this region but also to confirm two discussed regime shifts in the California current system. This new finding underlines the power of the proposed approach and promises new insights into other complex systems.

physics.data-an↗
arXiv2023

Universal bifurcation scenarios in delay-differential equations with one delay

We show that delay-differential equations (DDE) exhibit universal bifurcation scenarios, which are observed in large classes of DDEs with a single delay. Each such universality class has the same sequence of stabilizing or destabilizing Hopf bifurcations. These bifurcation sequences and universality classes can be explicitly described by using the asymptotic continuous spectrum for DDEs with large delays. Here, we mainly study linear DDEs, provide a general transversality result for the delay-induced bifurcations, and consider three most common universality classes. For each of them, we explicitly describe the sequence of stabilizing and destabilizing bifurcations. We also illustrate the implications for a nonlinear Stuart-Landau oscillator with time-delayed feedback.

math.DS↗
arXiv2023

Model adaptive phase space reconstruction

Phase space reconstruction (PSR) methods allow for the analysis of low-dimensional data with methods from dynamical system theory, but their application to prediction models, like those from machine learning (ML), is limited. Therefore, we present here a model adaptive phase space reconstruction (MAPSR) method that unifies the process of PSR with the modeling of the dynamical system. MAPSR is a differentiable PSR method that enables the use of ML methods and is based on the idea of time delay embedding. For achieving differentiable, continuous, real-valued delays, which can be optimized using gradient descent, the discrete time signal is converted to a continuous time signal. The delay vector, which stores all potential embedding delays and the trainable parameters of the model, are simultaneously updated to achieve an optimal time delay embedding for the observed system. MAPSR does not rely on any threshold or statistical criterion for determining the dimension and the set of delay values for the embedding process. The quality of the reconstruction is evaluated by the prediction loss. We apply the proposed approach to uni- and multivariate time series stemming from regular and chaotic dynamical systems and a turbulent combustor to test the generalizability of the method and compare our results with established PSR methods. We find that for the Lorenz system, the model trained with the MAPSR method is able to predict chaotic time series for nearly 7 to 8 Lyapunov time scales, which is found to be much better compared to other PSR methods (AMI-FNN and PECUZAL methods). For the univariate time series from the turbulent combustor, the long-term prediction error of the model trained using the MAPSR method stays in between that of AMI-FNN and PECUZAL methods for the regime of chaos, and for the regime of intermittency, the MAPSR method outperforms the AMI-FNN and PECUZAL methods.

physics.data-an↗
arXiv2023

Regional Greening as a `Positive' Tipping Phenomenon

Earth system tipping elements have been predominantly investigated for their potential to trigger \textit{negative} ecological, climatic, and societal shifts. Yet, an overlooked but seminal avenue exists in the form of \textit{positive} tipping phenomena, whose underlying mechanisms and benefits remain largely underexplored. To bridge this gap, our research introduces a fundamental percolation-based framework to assess the criticality and resilience of planetary terrestrial vegetation systems. Leveraging high-resolution satellite data, we focus on greening-induced positive tipping dynamics driven by global warming. We feature the Qinghai-Tibetan Plateau (QTP) and the Sahel region as contrasting yet analogous case studies. Our analysis uncovers an intriguing phenomenon where vegetation fragmentation aligns with a percolation threshold, exhibiting a scale-invariant pattern characterized by nearly perfect power laws with three critical exponents. Remarkably, contrary to conventional destructive tipping elements, these regions act as favorable tipping elements, transitioning from fragmented to cohesive vegetation patterns due to anthropogenic climate change and afforestation efforts. Furthermore, we propose an \textit{optimal resilience enhancement model} to reinforce vegetation robustness while minimizing socio-economic costs. This study provides valuable insights into the favorable aspects of tipping elements under climate change and offers effective strategies for enhancing ecological resilience against environmental threats.

physics.geo-ph↗
arXiv2023

Exotic swarming dynamics of high-dimensional swarmalators

Swarmalators are oscillators that can swarm as well as sync via a dynamic balance between their spatial proximity and phase similarity. We present a generalized D-dimensional swarmalator model, which is more realistic and versatile, that captures the self-organizing behaviors of a plethora of real-world collectives. This allows for modeling complicated processes such as flocking, schooling of fish, cell sorting during embryonic development, residential segregation, and opinion dynamics in social groups. We demonstrate its versatility by capturing the manoeuvers of the school of fish and traveling waves of gene expression, both qualitatively and quantitatively, embryonic cell sorting, microrobot collectives, and various life stages of slime mold by a suitable extension of the original model to incorporate appropriate features besides a gallery of its intrinsic self-organizations for various interactions. We expect this high-dimensional model to be potentially useful in describing swarming systems in a wide range of disciplines including physics of active matter, developmental biology, sociology, and engineering.

nlin.AO↗
arXiv2023

Emergence of Rigidity Percolation in Flowing Granular Systems

Jammed granular media and glasses exhibit spatial long-range correlations as a result of mechanical equilibrium. However, the existence of such correlations in the flowing matter, where the mechanical equilibrium is unattainable, has remained elusive. Here, we investigate this problem in the context of the percolation of interparticle forces in flowing granular media. We find that the flow rate introduces an effective long-range correlation, which plays the role of a relevant perturbation giving rise to a spectrum of varying exponents on a critical line as a function of the flow rate. Remarkably, our numerical simulations along with analytical arguments predict a crossover flow rate $\dotγ_c \simeq 10^{-5}$ below which the effect of induced disorder is weak and the universality of the force chain structure is shown to be given by the standard rigidity percolation. We also find a power-law behavior for the critical exponents with the flow rate $\dotγ>\dotγ_c$.

cond-mat.soft↗
arXiv2023

Time-reversible dynamics in a system of two coupled active rotators

We study two coupled active rotators with Kuramoto-type coupling and focus our attention to specific transitional regimes where the coupling is neither attractive nor repulsive. We show that certain such situations at the edge of synchronization can be characterized by the existence of a time-reversal symmetry of the system. We identify two different cases with such a time-reversal symmetry. The first case is characterized by a non-reciprocal attractive/repulsive coupling. The second case is a reciprocal coupling exactly at the edge between attraction and repulsion. We give a detailed description of possible different types of dynamics and bifurcations for both cases. In particular, we show how the time-reversible coupling can induce both oscillation death and oscillation birth to the active rotators. Moreover, we analyse the coexistence of conservative and dissipative regions in phase space, which is a typical feature of systems with a time-reversal symmetry. We show also, how perturbations breaking the time-reversal symmetry and destroying the conservative regions can lead to complicated types of dissipative dynamics such as the emergence of long-period cycles showing a bursting-like behavior.

math.DS↗
arXiv2023

Perspectives on adaptive dynamical systems

Adaptivity is a dynamical feature that is omnipresent in nature, socio-economics, and technology. For example, adaptive couplings appear in various real-world systems like the power grid, social, and neural networks, and they form the backbone of closed-loop control strategies and machine learning algorithms. In this article, we provide an interdisciplinary perspective on adaptive systems. We reflect on the notion and terminology of adaptivity in different disciplines and discuss which role adaptivity plays for various fields. We highlight common open challenges, and give perspectives on future research directions, looking to inspire interdisciplinary approaches.

nlin.AO↗
arXiv2023

Embedding Theory of Reservoir Computing and Reducing Reservoir Network Using Time Delays

Reservoir computing (RC), a particular form of recurrent neural network, is under explosive development due to its exceptional efficacy and high performance in reconstruction or/and prediction of complex physical systems. However, the mechanism triggering such effective applications of RC is still unclear, awaiting deep and systematic exploration. Here, combining the delayed embedding theory with the generalized embedding theory, we rigorously prove that RC is essentially a high dimensional embedding of the original input nonlinear dynamical system. Thus, using this embedding property, we unify into a universal framework the standard RC and the time-delayed RC where we novelly introduce time delays only into the network's output layer, and we further find a trade-off relation between the time delays and the number of neurons in RC. Based on this finding, we significantly reduce the network size of RC for reconstructing and predicting some representative physical systems, and, more surprisingly, only using a single neuron reservoir with time delays is sometimes sufficient for achieving those tasks.

cs.LG↗
arXiv2023

Adaptive Dynamical Networks

It is a fundamental challenge to understand how the function of a network is related to its structural organization. Adaptive dynamical networks represent a broad class of systems that can change their connectivity over time depending on their dynamical state. The most important feature of such systems is that their function depends on their structure and vice versa. While the properties of static networks have been extensively investigated in the past, the study of adaptive networks is much more challenging. Moreover, adaptive dynamical networks are of tremendous importance for various application fields, in particular, for the models for neuronal synaptic plasticity, adaptive networks in chemical, epidemic, biological, transport, and social systems, to name a few. In this review, we provide a detailed description of adaptive dynamical networks, show their applications in various areas of research, highlight their dynamical features and describe the arising dynamical phenomena, and give an overview of the available mathematical methods developed for understanding adaptive dynamical networks.

nlin.AO↗
arXiv2023

Rate and memory effects in bifurcation-induced tipping

A variation in the environment of a system, such as the temperature, the concentration of a chemical solution or the appearance of a magnetic field, may lead to a drift in one of the parameters. If the parameter crosses a bifurcation point, the system can tip from one attractor to another (bifurcation-induced tipping). Typically, this stability exchange occurs at a parameter value beyond the bifurcation value. This is what we call here the stability exchange shift. We study systematically how the shift is affected by the initial parameter value and its change rate. To that end, we present numerical and analytical results for different types of bifurcations and different paradigmatic systems. Finally, we deduce the scaling laws governing this phenomenon. We show that increasing the change rate and starting the drift further from the bifurcation can delay the tipping process. Furthermore, if the change rate is sufficiently small, the shift becomes independent of the initial condition (no memory) and the shift tends to zero as the square root of the change rate. Thus, the bifurcation diagram for the system with fixed parameters is recovered.

nlin.AO↗
arXiv2023

The dynamic nature of percolation on networks with triadic interactions

Percolation establishes the connectivity of complex networks and is one of the most fundamental critical phenomena for the study of complex systems. On simple networks, percolation displays a second-order phase transition; on multiplex networks, the percolation transition can become discontinuous. However, little is known about percolation in networks with higher-order interactions. Here, we show that percolation can be turned into a fully-fledged dynamical process when higher-order interactions are taken into account. By introducing signed triadic interactions, in which a node can regulate the interactions between two other nodes, we define triadic percolation. We uncover that in this paradigmatic model the connectivity of the network changes in time and that the order parameter undergoes a period-doubling and a route to chaos. We provide a general theory for triadic percolation which accurately predicts the full phase diagram on random graphs as confirmed by extensive numerical simulations. We find that triadic percolation on real network topologies reveals a similar phenomenology. These results radically change our understanding of percolation and may be used to study complex systems in which the functional connectivity is changing in time dynamically and in a non-trivial way, such as in neural and climate networks.

nlin.AO↗
arXiv2023

Stickiness and recurrence plots: an entropy-based approach

The stickiness effect is a fundamental feature of quasi-integrable Hamiltonian systems. We propose the use of an entropy-based measure of the recurrence plots (RP), namely, the entropy of the distribution of the recurrence times (estimated from the RP), to characterize the dynamics of a typical quasi-integrable Hamiltonian system with coexisting regular and chaotic regions. We show that the recurrence time entropy (RTE) is positively correlated to the largest Lyapunov exponent, with a high correlation coefficient. We obtain a multi-modal distribution of the finite-time RTE and find that each mode corresponds to the motion around islands of different hierarchical levels.

nlin.CD↗
arXiv2023

Extreme multistability in symmetrically coupled clocks

Extreme multistability (EM) is characterized by the emergence of infinitely many coexisting attractors or continuous families of stable states in dynamical systems. EM implies complex and hardly predictable asymptotic dynamical behavior. We analyse a model for pendulum clocks coupled by springs and suspended on an oscillating base, and show how EM can be induced in this system by a specifically designed coupling. First, we uncover that symmetric coupling can increase the dynamical complexity. In particular, the coexistence of multiple isolated attractors and continuous families of stable periodic states is generated in a symmetric cross-coupling scheme of four pendulums. These coexisting infinitely many states are characterized by different levels of phase synchronization between the pendulums, including anti-phase and in-phase states. Some of the states are characterized by splitting of the pendulums into groups with silent sub-threshold and oscillating behavior, respectively. The analysis of the basins of attraction further reveals the complex dependence of EM on initial conditions.

nlin.AO↗
arXiv2023

Dynamic Arctic weather variability and connectivity

The rapidly shrinking Arctic sea ice is changing weather patterns and disrupting the balance of nature. Dynamics of Arctic weather variability (WV) plays a crucial role in weather forecasting and is closely related to extreme weather events. Yet, assessing and quantifying the WV for both local Arctic regions and its planetary impacts under anthropogenic climate change is still unknown. Here, we develop a complexity-based approach to systematically evaluate and analyze the dynamic behaviour of WV. We reveal that the WV within and around the Arctic is statistically correlated to the Arctic Oscillation at the intraseasonal time scale. We further find that the variability of the daily Arctic sea ice is increasing due to its dramatic decline under a warming climate. Unstable Arctic weather conditions can disturb regional weather patterns through atmospheric teleconnection pathways, resulting in higher risk to human activities and greater weather forecast uncertainty. A multivariate climate network analysis reveals the existence of such teleconnections and implies a positive feedback loop between the Arctic and global weather instabilities. This enhances the mechanistic understanding of the influence of Arctic amplification on mid-latitude severe weather. Our framework provides a fresh perspective on the linkage of complexity science, WV and the Arctic.

physics.ao-ph↗