Maintaining stability in feedback systems, from aircraft and autonomous robots to biological and physiological systems, relies on monitoring their behavior and continuously adjusting their inputs. Incremental damage can make such control fragile. This tends to go unnoticed until a small perturbation induces instability (i.e., loss of control). Traditional methods in the field of engineering rely on accurate system models to compute a safe set of operating instructions, which become invalid when the, possibly damaged, system diverges from its model. Here we demonstrate that the approach of such a feedback system toward instability can nonetheless be monitored through dynamical indicators of resilience. This holistic system safety monitor does not rely on a system model and is based on the generic phenomenon of critical slowing down, shown to occur in the climate, biology, and other complex nonlinear systems approaching criticality. Our findings for engineered devices opens up a wide range of applications involving real-time early warning systems as well as an empirical guidance of resilient system design exploration, or “tinkering.” While we demonstrate the validity using drones, the generic nature of the underlying principles suggest that these indicators could apply across a wider class of controlled systems including reactors, aircraft, and self-driving cars.

A well-functioning society requires well-functioning institutions that ensure prosperity, fair distribution of wealth, social participation, security, and informative media. Such institutions are built on a foundation of trust. However, while trust is essential for economic success and good governance, interconnected mechanisms inherent in weakly governed market economies tend to undermine the very trust on which such success depends. These mechanisms include the intrinsic tendency for inequality to grow, media to boost perceived unfairness, and self-interest to gain rewards at the expense of others. These mechanisms, if left unchecked, allow wealth concentration to result in state capture where institutions facilitate further wealth concentration instead of the promoting the common good. As a result, people may become alienated and untrusting of fellow citizens and of institutions. Several democracies now experience such dynamics, the United States being a prime example. We discuss ways in which well-functioning democracies can design institutions to help avoid this social trap, and the much harder challenge of escaping the trap once in it. Successful cases such as the ability of Scandinavian democracies to maintain high-trust, and the US progressive era in the early 20th century provide instructive examples.

Climate change will worsen conditions for people in the Global South, while conditions in large parts of the North will improve. Migration seems an effective adaptation strategy. However, making that a win-win for migrants and receiving communities requires revision of the food system, rules for mobility, and strategies for social integration.

The possibility to anticipate critical transitions through detecting loss of resilience has attracted attention in many fields. Resilience indicators rely on the mathematical concept of critical slowing down, which means that a system recovers more slowly from external perturbations when it gets closer to tipping point. This decrease in recovery rate can be reflected in rising autocorrelation and variance in data. To test whether resilience is changing, resilience indicators are often calculated using a moving window in long, continuous time series of the system. However, for some systems, it may be more feasible to collect several high-resolution time series in short periods of time, i.e., in bursts. Resilience indicators can then be calculated to detect a change of resilience between such bursts. Here, we compare the performance of both methods using simulated data and showcase the possible use of bursts in a case study using mood data to anticipate depression in a patient. With the same number of data points, the burst approach outperformed the moving window method, suggesting that it is possible to downsample the continuous time series and still signal an upcoming transition. We suggest guidelines to design an optimal sampling strategy. Our results imply that using bursts of data instead of continuous time series may improve the capacity to detect changes in resilience. This method is promising for a variety of fields, such as human health, epidemiology, or ecology, where continuous monitoring can be costly or unfeasible.

Importance:Psychiatric disorders may come and go with symptoms changing over a lifetime. This suggests the need for a paradigm shift in diagnosis and treatment. Here we present a fresh look inspired by dynamical systems theory. This theory is used widely to explain tipping points, cycles, and chaos in complex systems ranging from the climate to ecosystems. Observations:In the dynamical systems view, we propose the healthy state has a basin of attraction representing its resilience, while disorders are alternative attractors in which the system can become trapped. Rather than an immutable trait, resilience in this approach is a dynamical property. Recent work has demonstrated the universality of generic dynamical indicators of resilience that are now employed globally to monitor the risks of collapse of complex systems, such as tropical rainforests and tipping elements of the climate system. Other dynamical systems tools are used in ecology and climate science to infer causality from time series. Moreover, experiences in ecological restoration confirm the theoretical prediction that under some conditions, short interventions may invoke long-term success when they flip the system into an alternative basin of attraction. All this implies practical applications for psychiatry, as are discussed in part 2 of this article. Conclusions and Relevance:Work in the field of dynamical systems points to novel ways of inferring causality and quantifying resilience from time series. Those approaches have now been tried and tested in a range of complex systems. The same tools may help monitoring and managing resilience of the healthy state as well as psychiatric disorders.

AbstractFew disagree that we should pass on the Earth in good shape to future generations, and many scientists want their work to contribute to that goal. Recent work has shown that hopelessness stands in the way of people taking an active attitude. At the same time, it is becoming clear what can be done about that: providing compelling visions of attractive futures and highlighting feasible pathways. Currently, science and the humanities are not well designed for this task. Practices that stand in the way of a more holistic change‐making approach include proposal‐based funding, paralyzing rigor requirements, and a focus on explanation rather than action. Removing those barriers may require culture shifts, a notoriously difficult and slow kind of change. Meanwhile, realistic inspiring future scenarios can be developed by bringing diverse thinkers together in environments where time, space, and immediate outcomes are not pressing.

Tipping points and alternative attractors have become an important focus of research and public discussions about the future of climate, ecosystems and societies. However, empirical evidence for the existence of alternative attractors remains scarce. For example, bimodal frequency distributions of state variables may suggest bistability, but can also be due to bimodality in external conditions. Here, we bring a new dimension to the classical arguments on alternative stable states and their resilience showing that the stochastic regime can distort the relationship between the probability distribution of states and the underlying attractors. Simple additive Gaussian white noise produces a one-to-one correspondence between the modes of frequency distributions and alternative stable states. However, for more realistic types of noise, the number and position of modes of the frequency distribution do not necessarily match the equilibria of the underlying deterministic system. We show that data must represent the stochastic regime as thoroughly as possible. When data are adequate then existing methods can be used to determine the nature of the underlying deterministic system and noise simultaneously. This may help resolve the question of whether there are tipping points, but also how realized states of a system are shaped by stochastic forcing vs internal stability properties. Open Research Statement Data and MATLAB codes for results reported here are available in the Github repository (Babak M. S. Arani 2023) The original data source is cited in the text. ### Competing Interest Statement The authors have declared no competing interest.

Potential analysis is used in many ecological studies to infer whether or not an ecosystem can have alternative stable states, to estimate the tipping points and, to assess the resilience of ecosystems. The main reason behind its frequent use is that such a frequency-based analysis is a minimalistic modelling strategy and therefore, is well-suited for limited ecological data with measurement errors. It has been used extensively in tree cover studies to discern alternative states of savannah and forest, the regime upon which savannah and forest coexist and, their corresponding resilience. Classical potential analysis may produce biased results due to inherent theoretical and practical limitations. This letter introduces a more sophisticated approach to address these shortcomings and enhance predictive capabilities regarding ecological dynamics, especially when working with insufficient data whose incorrect analysis can significantly impact management strategies. ### Competing Interest Statement The authors have declared no competing interest.

The Paleocene-Eocene Thermal Maximum (PETM; 56 Ma) and Eocene Thermal Maximum 2 and 3 (ETM2; 54.06 Ma and ETM3; 52.87 Ma) were three of a series of abrupt climate and carbon cycle perturbations, characterized by massive carbon input into the ocean-atmosphere system and strong global warming. These abrupt events, termed hyperthermals, potentially represent ‘tipping points’ at moments in time when the resilience of the system was low and reinforced by strong internal feedbacks, such as the catastrophic release of carbon from submarine methane hydrates. Alternatively, external mechanisms such as volcanism may have played a pronounced external role during the PETM. Here, we evaluate if the hyperthermals indeed resulted from reduced Earth System resilience and tipping point behaviour through the mathematical analyses of climate and carbon cycle indicators, namely, oxygen and stable carbon isotope ratios of deep ocean foraminifer calcite, across the late Paleocene and early Eocene. Our combined analysis using Dynamic Indicators of Resilience (DIORs) and Convergent Cross Mapping (CCM) reveals a loss of resilience and an increase in the causal interaction between the carbon cycle and climate towards the PETM, ETM2, and ETM3. A novel, windowed CCM approach indicates a tight coupling between carbon and climate across the early Eocene, further supporting dominant climate forcing on carbon cycle dynamics. This indicates that the internal rather than external mechanisms were responsible for the hyperthermals, suggesting a secondary role for endogenic processes such as volcanism. Furthermore, the CCM analysis in conjunction with the absence of major positive feedbacks such as the presence of polar ice caps during early Eocene could be employed to stipulate that these hyperthermal events may be caused by the increase in coupling between the carbon cycle and climate systems, eventually pushing both systems towards a tipping point through increasing positive feedbacks.

The boreal forest biome is warming four times faster than the global average. Changes so far are moderate, but time lags in responses may transiently maintain forest states which are no longer supported by current environmental conditions. Here, we explore whether tree cover dynamics hint at the state to which the biome may be shifting. Our results suggest that global boreal tree cover is heading for a unimodal state of open forest (30 to 50%), contrasting starkly to the bimodal distribution of dense forests (>60%) and sparse woodlands (5 to 15%) found today. A future open forest in a warmer world would likely increase the risk of forest fires, leading to potentially substantial releases of stored carbon.

Transformational change is possible, but design and implementation must seek to avoid lock-in.

The network theory of psychopathology posits that mental disorders are complex systems of mutually reinforcing symptoms. This overarching framework has proven highly generative but does not specify precisely how any specific mental disorder operates as such a system. We address this gap in the literature by developing a network theory of Panic Disorder and formalizing that theory as a computational model. We first review prior psychological theory and research on Panic Disorder in order to identify its core components as well as the plausible causal relations among those components. We then construct and evaluate a computational model of Panic Disorder as a non-linear dynamical system. We show that this model can explain a great deal, including individual differences in the propensity to experience panic attacks, key phenomenological characteristics of those attacks, the onset of Panic Disorder, and the efficacy of cognitive behavioral therapy. We also show that the model identifies significant gaps in our understanding of Panic Disorder and propose a theory-driven research agenda for Panic Disorder that follows from our evaluation of the model. We conclude by discussing the implications of the model for how we understand and investigate mental disorders as complex systems.

The potential collapse of the Atlantic Meridional Overturning Circulation (AMOC) poses substantial climate risks 1, yet some current economic models estimate it would have a net economic benefit through counteracting the impacts of global warming that led to its collapse in the first place 2–4. This is based on eventual net effects on country-level mean annual temperature 5,6, with no consideration of effects on precipitation, spatial detail, or shifting directions of climate change. Here, we explore the impacts of consecutive climate shifts on the human climate niche 7,8 – first 2.5°C global warming, disproportionately affecting the Global South, and then a collapse of the AMOC, impacting North Atlantic adjacent landmasses the most. We show that these sequential changes have very different spatial patterns of precipitation and temperature effects, some of which offset each other, while others are compounding. This represents a first step towards a more nuanced, spatially and temporally explicit approach to the quantification of the impacts of tipping a critical component of the climate system.

River deltas are susceptible to rapid and irreversible regime shifts in channel morphodynamics, estuarine turbidity and coastal wetland state. In this Review, we discuss the tipping mechanisms and self-reinforcing feedbacks underlying these regime shifts. The propensity for tipping in deltas can be increased by climate and land-use changes, based on projections from published data from 47 deltas worldwide. For example, sand mining, sediment retention behind barriers and increased floods under climate change have led to scour hole formation in the Rhine–Meuse Delta, river bank retreat in the Mekong Delta, and turbidity flushing in San Francisco Bay. Conversely, flood-prone areas with increased sediment influx caused by deforestation might be susceptible to avulsion. Resilience indicators based on observational data quantify the robustness of deltas to such regime shifts and could provide warnings when action should be taken to avoid degradation or yield insight into ways to promote back-tipping. However, resilience indicators alone are insufficient to identify the exact tipping point. Dynamical systems theory could provide a helpful framework to analyse tipping dynamics, but to apply this approach to real-world data, improvements in mathematical models of tipping points will be needed alongside an increase in continuous measurements of river deltas. Land-use and climate changes can reduce the resilience of river deltas to regime shifts in channel morphodynamics, estuarine turbidity and the state of coastal wetlands. This Review discusses how these regime shifts can be triggered, monitored and prevented.

Complex systems ranging from societies to ecological communities and power grids may be viewed as networks of connected elements. Such systems can go through critical transitions driven by an avalanche of contagious change. Here we ask, where in a complex network such a systemic shift is most likely to start. Intuitively, a central node seems the most likely source of such change. Indeed, topological studies suggest that central nodes can be the Achilles heel for attacks. We argue that the opposite is true for the class of networks in which all nodes tend to follow the state of their neighbors, a category we call two-way pull networks. In this case, a well-connected central node is an unlikely starting point of a systemic shift due to the buffering effect of connected neighbors. As a result, change is most likely to cascade through the network if it spreads first among relatively poorly connected nodes in the periphery. The probability of such initial spread is highest when the perturbation starts from intermediately connected nodes at the periphery, or more specifically, nodes with intermediate degree and relatively low closeness centrality. Our finding is consistent with empirical observations on social innovation, and may be relevant to topics as different as the sources of originality of art, collapse of financial and ecological networks and the onset of psychiatric disorders.

Using data from a wide range of natural communities including the human microbiome, plants, fish, mushrooms, rodents, beetles, and trees, we show that universally just a few percent of the species account for most of the biomass. This is in line with the classical observation that the vast bulk of biodiversity is very rare. Attempts to find traits allowing the tiny fraction of abundant species to escape rarity have remained unsuccessful. Here, we argue that this might be explained by the fact that hyper-dominance can emerge through stochastic processes. We demonstrate that in neutrally competing groups of species, rarity tends to become a trap if environmental fluctuations result in gains and losses proportional to abundances. This counter-intuitive phenomenon arises because absolute change tends to zero for very small abundances, causing rarity to become a “sticky state”, a pseudoattractor that can be revealed numerically in classical ball-in-cup landscapes. As a result, the vast majority of species spend most of their time in rarity leaving space for just a few others to dominate the neutral community. However, fates remain stochastic. Provided that there is some response diversity, roles occasionally shift as stochastic events or natural enemies bring an abundant species down allowing a rare species to rise to dominance. Microbial time series spanning thousands of generations support this prediction. Our results suggest that near-neutrality within niches may allow numerous rare species to persist in the wings of the dominant ones. Stand-ins may serve as insurance when former key species collapse.

How states and great powers rise and fall is an intriguing enigma of human history. Are there any patterns? Do polities become more vulnerable over time as they age? We analyze longevity in hundreds of premodern states using survival analysis to help provide initial insights into these questions. This approach is commonly used to study the risk of death in biological organisms or failure in mechanical systems. The results reveal that the risk of state termination increased steeply over approximately the first two centuries after formation and stabilized thereafter. This provides the first quantitative support for the hypothesis that the resilience of political states decreases over time. Potential mechanisms that could drive such declining resilience include environmental degradation, increasing complexity, growing inequality, and extractive institutions. While the cases are from premodern times, such dynamics and drivers of vulnerability may remain relevant today.

To reduce the consequences of infectious disease outbreaks, the timely implementation of public health measures is crucial. Currently used early-warning systems are highly context-dependent and require a long phase of model building. A proposed solution to anticipate the onset or termination of an outbreak is the use of so-called resilience indicators. These indicators are based on the generic theory of critical slowing down and require only incidence time series. Here we assess the potential for this approach to contribute to outbreak anticipation. We systematically reviewed studies that used resilience indicators to predict outbreaks or terminations of epidemics. We identified 37 studies meeting the inclusion criteria: 21 using simulated data and 16 real-world data. 36 out of 37 studies detected significant signs of critical slowing down before a critical transition (i.e., the onset or end of an outbreak), with a highly variable sensitivity (i.e., the proportion of true positive outbreak warnings) ranging from 0.03 to 1 and a lead time ranging from 10 days to 68 months. Challenges include low resolution and limited length of time series, a too rapid increase in cases, and strong seasonal patterns which may hamper the sensitivity of resilience indicators. Alternative types of data, such as Google searches or social media data, have the potential to improve predictions in some cases. Resilience indicators may be useful when the risk of disease outbreaks is changing gradually. This may happen, for instance, when pathogens become increasingly adapted to an environment or evolve gradually to escape immunity. High-resolution monitoring is needed to reach sufficient sensitivity. If those conditions are met, resilience indicators could help improve the current practice of prediction, facilitating timely outbreak response. We provide a step-by-step guide on the use of resilience indicators in infectious disease epidemiology, and guidance on the relevant situations to use this approach.

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