arXiv subjects

Jobst Heitzig

Publications and source records attributed to Jobst Heitzig.

At least 55 records · Page 3Linked to original sources

arXiv2020

A network-based microfoundation of Granovetter's threshold model for social tipping

Social tipping, where minorities trigger larger populations to engage in collective action, has been suggested as one key aspect in addressing contemporary global challenges. Here, we refine Granovetter's widely acknowledged theoretical threshold model of collective behavior as a numerical modelling tool for understanding social tipping processes and resolve issues that so far have hindered such applications. Based on real-world observations and social movement theory, we group the population into certain or potential actors, such that -- in contrast to its original formulation -- the model predicts non-trivial final shares of acting individuals. Then, we use a network cascade model to explain and analytically derive that previously hypothesized broad threshold distributions emerge if individuals become active via social interaction. Thus, through intuitive parameters and low dimensionality our refined model is adaptable to explain the likelihood of engaging in collective behavior where social tipping like processes emerge as saddle-node bifurcations and hysteresis.

physics.soc-ph↗

arXiv2020

Impact of Network Topology on the Stability of DC Microgrids

We probe the stability of Watts-Strogatz DC microgrids, in which droop-controlled producers and constant power load consumers are homogeneously distributed and obey Kirchhoff's circuit laws. The concept of survivability is employed to evaluate the system's response to Dirac delta voltage perturbations at single nodes. A fixed point analysis of the power grid model yields that there is only one relevant attractor. Using a set of simulations with random networks we investigate correlations between survivability and three topological network measures: the share of producers in the network and the degree and the average neighbour degree of the perturbed node. Depending on the imposed voltage and current limits, the stability is optimized for low node degrees or a specific share of producers. Based on our findings, we provide an insight into the local dynamics of the perturbed system and derive explicit guidelines for the design of resilient DC power grids.

physics.soc-ph↗

arXiv2019

Domino Effects in the Earth System -- The potential role of wanted tipping points

Vital parts of the climate system, such as the West Antarctic Ice Sheet, are at risk even within the aspired aims of the Paris Agreement to limit global temperature rise to 1.5 -- 2°C. These so-called natural tipping elements are characterized by rapid qualitative shifts in their states once a critical threshold, e.g., of global mean temperature, is transgressed. We argue that the prevention of such unwanted tipping through effective climate policies may critically depend on cascading Domino effects from (anticipated) climate impacts to emission reductions via wanted social tipping in attitudes, behaviors and policies. Specifically, the latter has recently been noted as a key aspect in addressing contemporary global challenges, such as climate change, via self-amplifying positive feedbacks similar to the processes observable in climate tipping elements. Our discussion is supported with data on commonly observed linkages between (subjective) climate change knowledge, concern and consequential potential action and we argue that the presence of such interrelations serves as a necessary condition for the possibility of rapid climate action.

physics.soc-ph↗

arXiv2019

Earth system modeling with endogenous and dynamic human societies: the copan:CORE open World-Earth modeling framework

Analysis of Earth system dynamics in the Anthropocene requires to explicitly take into account the increasing magnitude of processes operating in human societies, their cultures, economies and technosphere and their growing feedback entanglement with those in the physical, chemical and biological systems of the planet. However, current state-of-the-art Earth System Models do not represent dynamic human societies and their feedback interactions with the biogeophysical Earth system and macroeconomic Integrated Assessment Models typically do so only with limited scope. This paper (i) proposes design principles for constructing World-Earth Models (WEM) for Earth system analysis of the Anthropocene, i.e., models of social (World) - ecological (Earth) co-evolution on up to planetary scales, and (ii) presents the copan:CORE open simulation modeling framework for developing, composing and analyzing such WEMs based on the proposed principles. The framework provides a modular structure to flexibly construct and study WEMs. These can contain biophysical (e.g. carbon cycle dynamics), socio-metabolic/economic (e.g. economic growth) and socio-cultural processes (e.g. voting on climate policies or changing social norms) and their feedback interactions, and are based on elementary entity types, e.g., grid cells and social systems. Thereby, copan:CORE enables the epistemic flexibility needed for contributions towards Earth system analysis of the Anthropocene given the large diversity of competing theories and methodologies used for describing socio-metabolic/economic and socio-cultural processes in the Earth system by various fields and schools of thought. To illustrate the capabilities of the framework, we present an exemplary and highly stylized WEM implemented in copan:CORE that illustrates how endogenizing socio-cultural processes and feedbacks could fundamentally change macroscopic model outcomes.

physics.soc-ph↗

arXiv2019

Deep reinforcement learning in World-Earth system models to discover sustainable management strategies

Increasingly complex, non-linear World-Earth system models are used for describing the dynamics of the biophysical Earth system and the socio-economic and socio-cultural World of human societies and their interactions. Identifying pathways towards a sustainable future in these models for informing policy makers and the wider public, e.g. pathways leading to a robust mitigation of dangerous anthropogenic climate change, is a challenging and widely investigated task in the field of climate research and broader Earth system science. This problem is particularly difficult when constraints on avoiding transgressions of planetary boundaries and social foundations need to be taken into account. In this work, we propose to combine recently developed machine learning techniques, namely deep reinforcement learning (DRL), with classical analysis of trajectories in the World-Earth system. Based on the concept of the agent-environment interface, we develop an agent that is generally able to act and learn in variable manageable environment models of the Earth system. We demonstrate the potential of our framework by applying DRL algorithms to two stylized World-Earth system models. Conceptually, we explore thereby the feasibility of finding novel global governance policies leading into a safe and just operating space constrained by certain planetary and socio-economic boundaries. The artificially intelligent agent learns that the timing of a specific mix of taxing carbon emissions and subsidies on renewables is of crucial relevance for finding World-Earth system trajectories that are sustainable on the long term.

physics.soc-ph↗

arXiv2019

Emergent inequality and endogenous dynamics in a simple behavioral macroeconomic model

Standard macroeconomic models assume that households are rational in the sense that they are perfect utility maximizers, and explain economic dynamics in terms of shocks that drive the economy away from the stead-state. Here we build on a standard macroeconomic model in which a single rational representative household makes a savings decision of how much to consume or invest. In our model households are myopic boundedly rational heterogeneous agents embedded in a social network. From time to time each household updates its savings rate by copying the savings rate of its neighbor with the highest consumption. If the updating time is short, the economy is stuck in a poverty trap, but for longer updating times economic output approaches its optimal value, and we observe a critical transition to an economy with irregular endogenous oscillations in economic output, resembling a business cycle. In this regime households divide into two groups: Poor households with low savings rates and rich households with high savings rates. Thus inequality and economic dynamics both occur spontaneously as a consequence of imperfect household decision making. Our work here supports an alternative program of research that substitutes utility maximization for behaviorally grounded decision making.

econ.GN↗

arXiv2019

Divestment may burst the carbon bubble if investors' beliefs tip to anticipating strong future climate policy

To achieve the ambitious aims of the Paris climate agreement, the majority of fossil-fuel reserves needs to remain underground. As current national government commitments to mitigate greenhouse gas emissions are insufficient by far, actors such as institutional and private investors and the social movement on divestment from fossil fuels could play an important role in putting pressure on national governments on the road to decarbonization. Using a stochastic agent-based model of co-evolving financial market and investors' beliefs about future climate policy on an adaptive social network, here we find that the dynamics of divestment from fossil fuels shows potential for social tipping away from a fossil-fuel based economy. Our results further suggest that socially responsible investors have leverage: a small share of 10--20\,\% of such moral investors is sufficient to initiate the burst of the carbon bubble, consistent with the Pareto Principle. These findings demonstrate that divestment has potential for contributing to decarbonization alongside other social movements and policy instruments, particularly given the credible imminence of strong international climate policy. Our analysis also indicates the possible existence of a carbon bubble with potentially destabilizing effects to the economy.

q-fin.GN↗

arXiv2018

Dimension-scalable recurrence threshold estimation

The appropriate selection of recurrence thresholds is a key problem in applications of recurrence quantification analysis (RQA) and related methods across disciplines. Here, we discuss the distribution of pairwise distances between state vectors in the studied system's state space reconstructed by means of time-delay embedding as the key characteristic that should guide the corresponding choice for obtaining an adequate resolution of a recurrence plot. Specifically, we present an empirical description of the distance distribution, focusing on characteristic changes of its shape with increasing embedding dimension. Based on our results, we recommend selecting the recurrence threshold adaptively according to a fixed quantile of this distribution. We highlight the advantages of this strategy over other previously suggested approaches by discussing the performance of selected RQA measures in detecting chaos--chaos transitions in some prototypical model system.

physics.data-an↗

arXiv2017

The Contribution of Different Electric Vehicle Control Strategies to Dynamical Grid Stability

A major challenge for power grids with a high share of renewable energy systems (RES), such as island grids, is to provide frequency stability in the face of renewable fluctuations. In this work we evaluate the ability of electric vehicles (EV) to provide distributed primary control and to eliminate frequency peaks. To do so we for the first time explicitly model the network structure and incorporate non-Gaussian, strongly intermittent fluctuations typical for RES. We show that EVs can completely eliminate frequency peaks. Using threshold randomization we further demonstrate that demand synchronization effects and battery stresses can be greatly reduced. In contrast, explicit frequency averaging has a strong destabilizing effect, suggesting that the role of delays in distributed control schemes requires further studies. Overall we find that distributed control outperforms central one. The results are robust against a further increase in renewable power production and fluctuations.

physics.soc-ph↗

arXiv2017

Comparison of electricity market designs for stable decentralized power grids

In this study, we develop a theoretical model of strategic equilibrium bidding and price-setting behaviour by heterogeneous and boundedly rational electricity producers and a grid operator in a single electricity market under uncertain information about production capabilities and electricity demand. We compare eight different market design variants and several levels of centralized electricity production that influence the spatial distribution of producers in the grid, their unit production and curtailment costs, and the mean and standard deviation of their production capabilities. Our market design variants differ in three aspects. Producers are either paid their individual bid price ("pay as bid") or the (higher) market price set by the grid operator ("uniform pricing"). They are either paid for their bid quantity ("pay requested") or for their actual supply ("pay supplied") which may differ due to production uncertainty. Finally, excess production is either required to be curtailed or may be supplied to the grid. Overall, we find the combination of uniform pricing, paying for requested amounts, and required curtailment to perform best or second best in many respects, and to provide the best compromise between the goals of low economic costs, low consumer costs, positive profits, low balancing, low workload, and honest bidding behaviour.

physics.soc-ph↗

arXiv2017

Sustainability, collapse and oscillations of global climate, population and economy in a simple World-Earth model

The Anthropocene is characterized by close interdependencies between the natural Earth system and the human society, posing novel challenges to model development. Here we present a conceptual model describing the long-term coevolution of natural and socioeconomic subsystems of Earth. While the climate is represented via a global carbon cycle, we use economic concepts to model socio-metabolic flows of biomass and fossil fuels between nature and society. A wellbeing-dependent parametrization of fertility and mortality governs human population dynamics. Our analysis focuses on assessing possible asymptotic states of the Earth system for a qualitative understanding of its complex dynamics rather than quantitative predictions. Low dimension and simple equations enable a parameter-space analysis allowing us to identify preconditions of several asymptotic states and hence fates of humanity and planet. These include a sustainable co-evolution of nature and society, a global collapse and everlasting oscillations. We consider scenarios corresponding to different socio-cultural stages of human history. The necessity of accounting for the "human factor" in Earth system models is highlighted by the fact that carbon stocks during the past centuries evolved opposing to what would "naturally" be expected on a planet without humans. The intensity of biomass use and the contribution of ecosystem services to human well-being are found to be crucial determinants of the asymptotic state in a biomass-only scenario. The capitalistic, fossil-based scenario reveals that trajectories with fundamentally different asymptotic states might still be almost indistinguishable during a very long transient phase. Given current population levels, our study also supports the claim that besides reducing the global demand for energy, only the extensive use of renewable energies may pave the way into a sustainable future.

physics.soc-ph↗

arXiv2016

A Network of Networks Approach to Interconnected Power Grids

We present two different approaches to model power grids as interconnected networks of networks. Both models are derived from a model for spatially embedded mono-layer networks and are generalised to handle an arbitrary number of network layers. The two approaches are distinguished by their use case. The static glue stick construction model yields a multi-layer network from a predefined layer interconnection scheme, i.e. different layers are attached with transformer edges. It is especially suited to construct multi-layer power grids with a specified number of nodes in and transformers between layers. We contrast it with a genuine growth model which we label interconnected layer growth model.

physics.soc-ph↗

arXiv2016

Deciphering the imprint of topology on nonlinear dynamical network stability

Coupled oscillator networks show a complex interrelations between topological characteristics of the network and the nonlinear stability of single nodes with respect to large but realistic perturbations. We extend previous results on these relations by incorporating sampling-based measures of the transient behaviour of the system, its survivability, as well as its asymptotic behaviour, its basin stability. By combining basin stability and survivability we uncover novel, previously unknown asymptotic states with solitary, desynchronized oscillators which are rotating with a frequency different from their natural one. They occur almost exclusively after perturbations at nodes with specific topological properties. More generally we confirm and significantly refine the results on the distinguished role tree-shaped appendices play for nonlinear stability. We find a topological classification scheme for nodes located in such appendices, that exactly separates them according to their stability properties, thus establishing a strong link between topology and dynamics. Hence, the results can be used for the identification of vulnerable nodes in power grids or other coupled oscillator networks. From this classification we can derive general design principles for resilient power grids. We find that striving for homogeneous network topologies facilitates a better performance in terms of nonlinear dynamical network stability. While the employed second-order Kuramoto-like model is parametrized to be representative for power grids, we expect these insights to transfer to other critical infrastructure systems or complex network dynamics appearing in various other fields.

nlin.CD↗

arXiv2016

Timing of Transients: Quantifying Reaching Times and Transient Behavior in Complex Systems

When quantifying the time spent in the transient of a complex dynamical system, the fundamental problem is that for a large class of systems the actual time for reaching an attractor is infinite. Common methods for dealing with this problem usually introduce three additional problems: non-invariance, physical interpretation, and discontinuities, calling for carefully designed methods for quantifying transients. In this article, we discuss how the aforementioned problems emerge and propose two novel metrics, Regularized Reaching Time ($T_{RR}$) and Area under Distance Curve (AUDIC), to solve them, capturing two complementary aspects of the transient dynamics. $T_{RR}$ quantifies the additional time (positive or negative) that a trajectory starting at a chosen initial condition needs to reach the attractor after a reference trajectory has already arrived there. A positive or negative value means that it arrives by this much earlier or later than the reference. Because $T_{RR}$ is an analysis of return times after shocks, it is a systematic approach to the concept of critical slowing down [1]; hence it is naturally an early-warning signal [2] for bifurcations when central statistics over distributions of initial conditions are used. AUDIC is the distance of the trajectory to the attractor integrated over time. Complementary to $T_{RR}$, it measures which trajectories are reluctant, i.e. stay away from the attractor for long, or eager to approach it right away. (... shortened for arxiv listing, full abstract in paper ...) New features in these models can be uncovered, including the surprising regularity of the Roessler system's basin of attraction even in the regime of a chaotic attractor. Additionally, we demonstrate the critical slowing down interpretation by presenting the metrics' sensitivity to prebifurcational change and thus how they act as early-warning signals.

nlin.CD↗

arXiv2016

Survivability of Deterministic Dynamical Systems

The notion of a part of phase space containing desired (or allowed) states of a dynamical system is important in a wide range of complex systems research. It has been called the safe operating space, the viability kernel or the sunny region. In this paper we define the notion of survivability: Given a random initial condition, what is the likelihood that the transient behaviour of a deterministic system does not leave a region of desirable states. We demonstrate the utility of this novel stability measure by considering models from climate science, neuronal networks and power grids. We also show that a semi-analytic lower bound for the survivability of linear systems allows a numerically very efficient survivability analysis in realistic models of power grids. Our numerical and semi-analytic work underlines that the type of stability measured by survivability is not captured by common asymptotic stability measures.

nlin.AO↗

arXiv2016

Macroscopic description of complex adaptive networks co-evolving with dynamic node states

In many real-world complex systems, the time-evolution of the network's structure and the dynamic state of its nodes are closely entangled. Here, we study opinion formation and imitation on an adaptive complex network which is dependent on the individual dynamic state of each node and vice versa to model the co-evolution of renewable resources with the dynamics of harvesting agents on a social network. The adaptive voter model is coupled to a set of identical logistic growth models and we show that in such systems, the rate of interactions between nodes as well as the adaptive rewiring probability play a crucial role for the sustainability of the system's equilibrium state. We derive a macroscopic description of the system which provides a general framework to model and quantify the influence of single node dynamics on the macroscopic state of the network and is applicable to many fields of study, such as epidemic spreading or social modeling.

physics.soc-ph↗

arXiv2016

Unified functional network and nonlinear time series analysis for complex systems science: The pyunicorn package

We introduce the \texttt{pyunicorn} (Pythonic unified complex network and recurrence analysis toolbox) open source software package for applying and combining modern methods of data analysis and modeling from complex network theory and nonlinear time series analysis. \texttt{pyunicorn} is a fully object-oriented and easily parallelizable package written in the language Python. It allows for the construction of functional networks such as climate networks in climatology or functional brain networks in neuroscience representing the structure of statistical interrelationships in large data sets of time series and, subsequently, investigating this structure using advanced methods of complex network theory such as measures and models for spatial networks, networks of interacting networks, node-weighted statistics or network surrogates. Additionally, \texttt{pyunicorn} provides insights into the nonlinear dynamics of complex systems as recorded in uni- and multivariate time series from a non-traditional perspective by means of recurrence quantification analysis (RQA), recurrence networks, visibility graphs and construction of surrogate time series. The range of possible applications of the library is outlined, drawing on several examples mainly from the field of climatology.

physics.data-an↗

arXiv2016

Potentials and Limits to Basin Stability Estimation

Stability assessment methods for dynamical systems have recently been complemented by basin stability and derived measures, i.e. probabilistic statements whether systems remain in a basin of attraction given a distribution of perturbations. This requires numerical estimation via Monte-Carlo sampling and integration of differential equations. Here, we analyze the applicability of basin stability to systems with basin geometries challenging for this numerical method, having fractal basin boundaries and riddled or intermingled basins of attraction. We find that numerical basin stability estimation is still meaningful for fractal boundaries but reaches its limits for riddled basins with holes.

nlin.CD↗