arXiv subjects

Marc Timme

Publications and source records attributed to Marc Timme.

At least 19 recordsLinked to original sources

arXiv2025

Hopf-Induced Desynchronization

The emergence of synchrony essentially underlies the functionality of many systems across physics, biology and engineering. In all established synchronization phase transitions so far, a stable synchronous state is connected to a stable incoherent state: For continuous transitions, stable synchrony directly connects to stable incoherence at a critical point, whereas for discontinuous transitions, stable synchrony is connected to stable incoherence via an additional unstable branch. Here we present a novel type of transition between synchrony and incoherence where the synchronous state does not connect to the state of incoherence. We uncover such transitions in the complexified Kuramoto model with their variables and coupling strength parameter analytically continued. Deriving a self-consistency equation for a quaternion order parameter that we propose helps to mathematically pin down the mechanisms underlying this transition type. Local numerical analysis suggests that the transition is linked to a Hopf bifurcation destabilizing synchrony, in contrast to branching point bifurcations established for the transition between synchrony and incoherence so far.

nlin.AO↗

arXiv2025

Extreme Synchronization Transitions

Across natural and human-made systems, transition points mark sudden changes of order and are thus key to understanding overarching system features. Motivated by recent experimental observations, we here uncover an intriguing class of transitions in coupled oscillators, extreme synchronization transitions, from asynchronous disordered states to synchronous states with almost completely ordered phases. Whereas such a transition appears like discontinuous or explosive phase transitions, it exhibits markedly distinct features. First, the transition occurs already in finite systems of $N$ units and so constitutes an intriguing bifurcation of multi-dimensional systems rather than a genuine phase transition that emerges in the thermodynamic limit $N\rightarrow \infty$ only. Second, the synchronization order parameter jumps from moderate values of the order of $N^{-1/2}$ to values extremely close to $1$, its theoretical maximum, immediately upon crossing a critical coupling strength. We analytically explain the mechanisms underlying such extreme transitions in coupled complexified Kuramoto oscillators. Extreme transitions may similarly occur across other systems of coupled oscillators as well as in certain percolation processes. In applications, their occurrence impacts our ability of ensuring or preventing strong forms of ordering, for instance in biological and engineered systems.

nlin.AO↗

arXiv2024

Synchrony for weak coupling in the complexified Kuramoto model

We present the finite-size Kuramoto model analytically continued from real to complex variables and analyze its collective dynamics. For strong coupling, synchrony appears through locked states that constitute attractors, as for the real-variable system. However, synchrony persists in the form of \textit{complex locked states} for coupling strengths $K$ below the transition $K^{(\text{pl})}$ to classical \textit{phase locking}. Stable complex locked states indicate a locked sub-population of zero mean frequency in the real-variable model and their imaginary parts help identifying which units comprise that sub-population. We uncover a second transition at $K'<K^{(\text{pl})}$ below which complex locked states become linearly unstable yet still exist for arbitrarily small coupling strengths.

nlin.AO↗

arXiv2024

Fluctuation Response Patterns of Network Dynamics -- an Introduction

Networked dynamical systems, i.e., systems of dynamical units coupled via nontrivial interaction topologies, constitute models of broad classes of complex systems, ranging from gene regulatory and metabolic circuits in our cells to pandemics spreading across continents. Most of such systems are driven by irregular and distributed fluctuating input signals from the environment. Yet how networked dynamical systems collectively respond to such fluctuations depends on the location and type of driving signal, the interaction topology and several other factors and remains largely unknown to date. As a key example, modern electric power grids are undergoing a rapid and systematic transformation towards more sustainable systems, signified by high penetrations of renewable energy sources. These in turn introduce significant fluctuations in power input and thereby pose immediate challenges to the stable operation of power grid systems. How power grid systems dynamically respond to fluctuating power feed-in as well as other temporal changes is critical for ensuring a reliable operation of power grids yet not well understood. In this work, we systematically introduce a linear response theory for fluctuation-driven networked dynamical systems. The derivations presented not only provide approximate analytical descriptions of the dynamical responses of networks, but more importantly, allows to extract key qualitative features about spatio-temporally distributed response patterns. Specifically, we provide a general formulation of a linear response theory for perturbed networked dynamical systems, explicate how dynamic network response patterns arise from the solution of the linearized response dynamics, and emphasize the role of linear response theory in predicting and comprehending power grid responses on different temporal and spatial scales and to various types of disturbances.

nlin.AO↗

arXiv2024

Topological Determinants of Perturbation Spreading in Networks

Spreading phenomena essentially underlie the dynamics of various natural and technological networked systems, yet how spatiotemporal propagation patterns emerge from such networks remains largely unknown. Here we propose a novel approach that reveals universal features determining the spreading dynamics in diffusively coupled networks and disentangles them from factors that are system specific. In particular, we first analytically identify a purely topological factor encoding the interaction structure and strength, and second, numerically estimate a master function characterizing the universal scaling of the perturbation arrival times across topologically different networks. The proposed approach thereby provides intuitive insights into complex propagation patterns as well as accurate predictions for the perturbation arrival times. The approach readily generalizes to a wide range of networked systems with diffusive couplings and may contribute to assess the risks of transient influences of ubiquitous perturbations in real-world systems.

physics.soc-ph↗

arXiv2024

Complexified Synchrony

The Kuramoto model and its generalizations have been broadly employed to characterize and mechanistically understand various collective dynamical phenomena, especially the emergence of synchrony among coupled oscillators. Despite almost five decades of research, many questions remain open, in particular for finite-size systems. Here, we generalize recent work [Phys. Rev. Lett. 130, 187201 (2023)] on the finite-size Kuramoto model with its state variables analytically continued to the complex domain and also complexify its system parameters. Intriguingly, systems of two units with purely imaginary coupling do not actively synchronize even for arbitrarily large magnitudes of the coupling strengths, $|K| \rightarrow \infty$, but exhibit conservative dynamics with asynchronous rotations or librations for all $|K|$. For generic complex coupling, both, traditional phase-locked states and asynchronous states generalize to complex locked states, fixed points off the real subspace that exist even for arbitrarily weak coupling. We analyze a new collective mode of rotations exhibiting finite, yet arbitrarily large rotation numbers. Numerical simulations for large networks indicate a novel form of discontinuous phase transition. We close by pointing to a range of exciting questions for future research.

nlin.AO↗

arXiv2023

Exponential Adoption of Battery Electric Cars

The adoption of battery electric vehicles (BEVs) may significantly reduce greenhouse gas emissions caused by road transport. However, there is wide disagreement as to how soon battery electric vehicles will play a major role in overall transportation. Focusing on battery electric passenger cars, we here analyze BEV adoption across 17 individual countries, Europe, and the World, and consistently find exponential growth trends. Modeling-based estimates of future adoption given past trends suggests system-wide adoption substantially faster than typical economic analyses have proposed so far. For instance, we estimate the majority of passenger cars in Europe to be electric by about 2031. Within regions, the predicted times of mass adoption are largely insensitive to model details. Despite significant differences in current electric fleet sizes across regions, their growth rates consistently indicate fast doubling times of approximately 15 months, hinting at radical economic and infrastructural consequences in the near future.

physics.soc-ph↗

arXiv2023

Taming Travel Time Fluctuations through Adaptive Stop Pooling

Ride sharing services combine trips of multiple users in the same vehicle and may provide more sustainable transport than private cars. As mobility demand varies during the day, the travel times experienced by passengers may substantially vary as well, making the service quality unreliable. We show through model simulations that such travel time fluctuations may be drastically reduced by stop pooling. Having users walk to meet at joint locations for pick-up or drop-off allows buses to travel more direct routes by avoiding frequent door-to-door detours, especially during high demand. We in particular propose adaptive stop pooling by adjusting the maximum walking distance to the temporally and spatially varying demand. The results highlight that adaptive stop pooling may substantially reduce travel time fluctuations while even improving the average travel time of ride sharing services, especially for high demand. Such quality improvements may in turn increase the acceptance and adoption of ride sharing services.

physics.soc-ph↗

arXiv2023

Identifying the threshold to sustainable ridepooling

Ridepooling combines trips of multiple passengers in the same vehicle and may thereby provide a more sustainable option than transport by private cars. The efficiency and sustainability of ridepooling is typically quantified by key performance indicators such as the average vehicle occupancy or the total distance driven by all ridepooling vehicles relative to individual transport. However, even if the average occupancy is high and rides are shared, ridepooling services may increase the total distance driven due to additional detours and deadheading. Moreover, these key performance indicators are difficult to predict without large-scale simulations or actual ridepooling operation. Here, we propose a dimensionless parameter to estimate the sustainability of ridepooling by quantifying the load on a ridepooling service, relating characteristic timescales of demand and supply. The load bounds the relative distance driven and uniquely marks the break-even point above which the total distance driven by all vehicles of a ridepooling service falls below that of motorized individual transport. Detailed event-based simulations and a comparison with empirical observations from a ridepooling pilot project in a rural area of Germany validate the theoretical prediction. Importantly, the load follows directly from a small set of aggregate parameters of the service setting and is thus predictable a priori. The load may thus complement standard key performance indicators and simplify planning, operation and evaluation of ridepooling services.

physics.soc-ph↗

arXiv2023

Recreational Mobility Prior and During the COVID-19 Pandemic

The COVID-19 pandemic and the resulting economic recession negatively affected many people's physical, social, and psychological health and has been shown to change population-level mobility, but little attention has been given to park visitations as an indicator. Estimating the frequency of park visitations from aggregated mobility data of all the parks in Washington State (USA), we study trends in park use one year prior to and two years during the COVID-19 pandemic. Our findings indicate that the gravity model is a robust model for the park visitation behavior in different spatial resolutions of city level and state level and different socio-economical classes. Incorporating network structure, our detailed analysis highlights that high-income level residents changed their recreational behavior by visiting their local parks more and a broader recreational options outside of their local census area; whereas the low-income residents changed their visitation behavior by reducing their recreational choices.

physics.soc-ph↗

arXiv2023

Equivalence of Additive and Multiplicative Coupling in Spiking Neural Networks

Spiking neural network models characterize the emergent collective dynamics of circuits of biological neurons and help engineer neuro-inspired solutions across fields. Most dynamical systems' models of spiking neural networks typically exhibit one of two major types of interactions: First, the response of a neuron's state variable to incoming pulse signals (spikes) may be additive and independent of its current state. Second, the response may depend on the current neuron's state and multiply a function of the state variable. Here we reveal that spiking neural network models with additive coupling are equivalent to models with multiplicative coupling for simultaneously modified intrinsic neuron time evolution. As a consequence, the same collective dynamics can be attained by state-dependent multiplicative and constant (state-independent) additive coupling. Such a mapping enables the transfer of theoretical insights between spiking neural network models with different types of interaction mechanisms as well as simpler and more effective engineering applications.

physics.comp-ph↗

arXiv2023

Volatile Memory Motifs: Minimal Spiking Neural Networks

How spiking neuronal networks encode memories in their different time and spatial scales constitute a fundamental topic in neuroscience and neuro-inspired engineering. Much attention has been paid to large networks and long-term memory, for example in models of associative memory. Smaller circuit motifs may play an important complementary role on shorter time scales, where broader network effects may be of less relevance. Yet, compact computational models of spiking neural networks that exhibit short-term volatile memory and actively hold information until their energy source is switched off, seem not fully understood. Here we propose that small spiking neural circuit motifs may act as volatile memory components. A minimal motif consists of only two interconnected neurons -- one self-connected excitatory neuron and one inhibitory neuron -- and realizes a single-bit volatile memory. An excitatory, delayed self-connection promotes a bistable circuit in which a self-sustained periodic orbit generating spike trains co-exists with the quiescent state of no neuron spiking. Transient external inputs may straightforwardly induce switching between those states. Moreover, the inhibitory neuron may act as an autonomous turn-off switch. It integrates incoming excitatory pulses until a threshold is reached after which the inhibitory neuron emits a spike that then inhibits further spikes in the excitatory neuron, terminating the memory. Our results show how external bits of information (excitatory signal), can be actively held in memory for a pre-defined amount of time. We show that such memory operations are robust against parameter variations and exemplify how sequences of multidimensional input signals may control the dynamics of a many-bits memory circuit in a desired way.

q-bio.NC↗

arXiv2022

Understanding Braess' Paradox in power grids

The ongoing energy transition requires power grid extensions to connect renewable generators to consumers and to transfer power among distant areas. The process of grid extension requires a large investment of resources and is supposed to make grid operation more robust. Yet, counter-intuitively, increasing the capacity of existing lines or adding new lines may also reduce the overall system performance and even promote blackouts due to Braess' paradox. Braess' paradox was theoretically modeled but not yet proven in realistically scaled power grids. Here, we present an experimental setup demonstrating Braess' paradox in an AC power grid and show how it constrains ongoing large-scale grid extension projects. We present a topological theory that reveals the key mechanism and predicts Braessian grid extensions from the network structure. These results offer a theoretical method to understand and practical guidelines in support of preventing unsuitable infrastructures and the systemic planning of grid extensions.

eess.SY↗

arXiv2022

Explosive Transitions in Epidemic Dynamics

Standard epidemic models exhibit one continuous, second order phase transition to macroscopic outbreaks. However, interventions to control outbreaks may fundamentally alter epidemic dynamics. Here we reveal how such interventions modify the type of phase transition. In particular, we uncover three distinct types of explosive phase transitions for epidemic dynamics with capacity-limited interventions. Depending on the capacity limit, interventions may (i) leave the standard second order phase transition unchanged but exponentially suppress the probability of large outbreaks, (ii) induce a first-order discontinuous transition to macroscopic outbreaks, or (iii) cause a secondary explosive yet continuous third-order transition. These insights highlight inherent limitations in predicting and containing epidemic outbreaks. More generally our study offers a cornerstone example of a third order explosive phase transition in complex systems.

physics.soc-ph↗

arXiv2022

Phase separation induces congestion waves in electric vehicle charging

Electric vehicles may dominate motorized transport in the next decade, yet the impact of the collective dynamics of electric mobility on long-range traffic flow is still largely unknown. We demonstrate a type of congestion that arises if charging infrastructure is limited or electric vehicle density is high. This congestion emerges solely through indirect interactions at charging infrastructure by queue-avoidance behavior that - counterintuitively - induces clustering of occupied charging stations and phase separation of the flow into free and congested stations. The resulting congestion waves always propagate forward in the direction of travel, in contrast to typically backward-propagating congestion waves known from traditional traffic jams. These results may guide the planning and design of charging infrastructure and decision support applications in the near future.

nlin.AO↗

arXiv2022

Collective dynamics of capacity-constrained ride-pooling fleets

Ride-pooling (or ride-sharing) services combine trips of multiple customers along similar routes into a single vehicle. The collective dynamics of the fleet of ride-pooling vehicles fundamentally underlies the efficiency of these services. In simplified models, the common features of these dynamics give rise to scaling laws of the efficiency that are valid across a wide range of street networks and demand settings. However, it is unclear how constraints of the vehicle fleet impact such scaling laws. Here, we map the collective dynamics of capacity-constrained ride-pooling fleets to services with unlimited passenger capacity and identify an effective fleet size of available vehicles as the relevant scaling parameter characterizing the dynamics. Exploiting this mapping, we generalize the scaling laws of ride-pooling efficiency to capacity-constrained fleets. We approximate the scaling function with a queueing theoretical analysis of the dynamics in a minimal model system, thereby enabling mean-field predictions of required fleet sizes in more complex settings. These results may help to transfer insights from existing ride-pooling services to new settings or service locations.

physics.soc-ph↗

arXiv2022

Demand-driven design of bicycle infrastructure networks for improved urban bikeability

Cycling is a crucial part of sustainable urban transportation. Promoting cycling critically relies on a sufficiently developed bicycle infrastructure. However, designing efficient bike path networks constitutes a complex problem that requires balancing multiple constraints while still supporting all cycling demand. Here, we propose a framework to create families of efficient bike path networks by explicitly taking into account the demand distribution and cyclists' route choices based on safety preferences. By reversing the network formation process and iteratively removing bike paths from an initially complete bike path network and continually updating cyclists' route choices, we create a sequence of networks that is always adapted to the current cycling demand. We illustrate the applicability of this demand-driven planning scheme for two cities. A comparison of the resulting bike path networks with those created for homogenized demand enables us to quantify the importance of the demand distribution for network planning. The proposed framework may thus enable quantitative evaluation of the structure of current and planned bike path networks and support the demand-driven design of efficient infrastructures.

physics.soc-ph↗

arXiv2022

Predicting Braess' Paradox in Supply and Transport Networks

Reliable functioning of supply and transport networks fundamentally support many non-equilibrium dynamical systems, from biological organisms and ecosystems to human-made water, gas, heat, electricity and traffic networks. Strengthening an edge of such a network lowers its resistance opposing a flow and intuitively improves the robustness of the system's function. If, in contrast, it deteriorate operation by overloading other edges, the counterintuitive phenomenon of \emph{Braess' paradox} emerges. How to predict which edges enhancements may trigger Braess' paradox remains unknown to date. To approximately locate and intuitively understand such Braessian edges, we here present a differential perspective on how enhancing any edge impacts network-wide flow patterns. First, we exactly map the prediction problem to a dual problem of electrostatic dipole currents on networks such that simultaneously finding \textit{all} Braessian edges is equivalent to finding the currents in the resistor network resulting from a constant current across one edge. Second, we propose a simple approximate criterion -- rerouting alignment -- to efficiently predict Braessian edges, thereby providing an intuitive topological understanding of the phenomenon. Finally, we show how to intentionally weaken Braessian edges to mitigate network overload, with beneficial consequences for network functionality.

nlin.AO↗