Bifurcation, stability, and critical slowing down in a simple mass–spring system

Bissell, J. J.

doi:10.1016/j.mechrescom.2022.103967

Cited by 4 publications

(2 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Moreover, at a low RA the variance of the state variable (calculated with a 5-year moving window) increased ( figure 3 c ). These results indicate that the resilience estimated by CUSPRA corresponds to the concept of resilience in ecology [ 4 , 46 , 62 , 63 ].…”

Section: Resultsmentioning

confidence: 72%

Resilience assessment in complex natural systems

Sguotti,

Vasilakopoulos,

Tzanatos

et al. 2024

Proc. R. Soc. B.

View full text Add to dashboard Cite

Ecological resilience is the capability of an ecosystem to maintain the same structure and function and avoid crossing catastrophic tipping points (i.e. undergoing irreversible regime shifts). While fundamental for management, concrete ways to estimate and interpret resilience in real ecosystems are still lacking. Here, we develop an empirical approach to estimate resilience based on the stochastic cusp model derived from catastrophe theory. The cusp model models tipping points derived from a cusp bifurcation. We extend cusp in order to identify the presence of stable and unstable states in complex natural systems. Our Cusp Resilience Assessment (CUSPRA) has three characteristics: (i) it provides estimates on how likely a system is to cross a tipping point (in the form of a cusp bifurcation) characterized by hysteresis, (ii) it assesses resilience in relation to multiple external drivers and (iii) it produces straightforward results for ecosystem-based management. We validate our approach using simulated data and demonstrate its application using empirical time series of an Atlantic cod population and marine ecosystems in the North Sea and the Mediterranean Sea. We show that Cusp Resilience Assessment is a powerful method to empirically estimate resilience in support of a sustainable management of our constantly adapting ecosystems under global climate change.

show abstract

Section: Resultsmentioning

confidence: 72%

Resilience assessment in complex natural systems

Sguotti,

Vasilakopoulos,

Tzanatos

et al. 2024

Proc. R. Soc. B.

View full text Add to dashboard Cite

show abstract

“…characteristic of critical transition is that a very small change in the parameters of the high-dimensional network system can result in a large shift of the equilibrium point, which is known as bifurcation [3]. Another remarkable observation of critical transition is that the recovery of a high-dimensional network system from small perturbations is extremely slow, which is called critical slowing down phenomenon [4], [5]. More specifically, for a high-dimensional network system whose linearized system has a Hurwitz matrix as the system matrix, the mathematical interpretation of critical slowing down is that the real part of the dominant eigenvalues (i.e., eigenvalues having the largest real part) of the system matrix is close to zero [6].…”

mentioning

confidence: 99%

Model-Free Dominant Pole Placement for Restabilizing High-Dimensional Network Systems via Small-Sample-Size Data

et al. 2023

View full text Add to dashboard Cite

There is a critical transition before a high-dimensional network system completely deteriorates. The Dynamical Network Marker (DNM) theory has been developed for the early prediction of such critical transitions by only using High-Dimension Small-Sample-Size (HDSSS) data. This article presents a model-free dominant pole placement approach for restabilizing the high-dimensional network systems towards avoidance of critical transitions by early treatment. Instead of traditional model-based pole placement, we present a model-free exact dominant pole placement method with dominant eigenvectors of the system matrix, which can be estimated from HDSSS data of system states. We further introduce two approximations of exact dominant pole placement to reduce the complexity of implementing restabilization. The first one is to approximate the right dominant eigenvector-based pole placement by reducing the number of intervened nodes. The second one is to intervene only in the diagonal part of the system matrix. We conduct theoretical analysis and numerical simulations to investigate the performance of the proposed dominant pole placement method.INDEX TERMS Data-driven control, matrix perturbation, pole placement. I. INTRODUCTION A. BACKGROUND AND MOTIVATION

show abstract

Sediment DNA Records the Critical Transition of Bacterial Communities in the Arid Lake

Hu,

Cai,

Song

et al. 2024

Microb Ecol

View full text Add to dashboard Cite

It is necessary to predict the critical transition of lake ecosystems due to their abrupt, non-linear effects on social-economic systems. Given the promising application of paleolimnological archives to tracking the historical changes of lake ecosystems, it is speculated that they can also record the lake’s critical transition. We studied Lake Dali-Nor in the arid region of Inner Mongolia because of the profound shrinking the lake experienced between the 1300 s and the 1600 s. We reconstructed the succession of bacterial communities from a 140-cm-long sediment core at 4-cm intervals and detected the critical transition. Our results showed that the historical trajectory of bacterial communities from the 1200 s to the 2010s was divided into two alternative states: state1 from 1200 to 1300 s and state2 from 1400 to 2010s. Furthermore, in the late 1300 s, the appearance of a tipping point and critical slowing down implied the existence of a critical transition. By using a multi-decadal time series from the sedimentary core, with general Lotka-Volterra model simulations, local stability analysis found that bacterial communities were the most unstable as they approached the critical transition, suggesting that the collapse of stability triggers the community shift from an equilibrium state to another state. Furthermore, the most unstable community harbored the strongest antagonistic and mutualistic interactions, which may imply the detrimental role of interaction strength on community stability. Collectively, our study showed that sediment DNA can be used to detect the critical transition of lake ecosystems.

show abstract

Bifurcation, stability, and critical slowing down in a simple mass–spring system

Cited by 4 publications

References 12 publications

Resilience assessment in complex natural systems

Resilience assessment in complex natural systems

Model-Free Dominant Pole Placement for Restabilizing High-Dimensional Network Systems via Small-Sample-Size Data

Sediment DNA Records the Critical Transition of Bacterial Communities in the Arid Lake

Contact Info

Product

Resources

About