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In many drylands around the globe, vegetation self-organizes into regular spatial patterns in response to aridity stress. We consider the regularly-spaced vegetation bands, on gentle hill-slopes, that survive low rainfall conditions by…

Pattern Formation and Solitons · Physics 2025-05-07 Punit Gandhi , Matthew Oline , Mary Silber

Rising interest in the resilience of ecological systems has spawned diverse interpretations of the term's precise meaning. This paper classifies and explores definitions of resilience from the ecological literature using a dynamical systems…

Dynamical Systems · Mathematics 2018-03-22 Katherine Meyer

This paper introduces a novel approach to quantifying ecological resilience in biological systems, particularly focusing on noisy systems responding to episodic disturbances with sudden adaptations. Incorporating concepts from…

Quantitative Methods · Quantitative Biology 2024-12-24 Jorge M. Ramirez , Juan M. Restrepo , Valerio Lucarini , David Weston

Resilience broadly describes a quality of withstanding perturbations. Measures of system resilience have gathered increasing attention across applied disciplines, yet existing metrics often lack computational accessibility and…

Dynamical Systems · Mathematics 2026-02-09 Andreas Morr , Christian Kuehn , George Datseris

Ecological resilience refers to the ability of a system to retain its state when subject to state variables perturbations or parameter changes. While understanding and quantifying resilience is crucial to anticipate the possible regime…

Dynamical Systems · Mathematics 2019-05-10 Artur César Fassoni , Denis de Carvalho Braga

Some ODE models treat ecological disturbance as a continuous process, even disturbances such as fire that occur almost instantaneously on the timescale of system recovery. Alternatively, flow-kick models resolve disturbances as discrete…

Dynamical Systems · Mathematics 2024-12-09 Katherine Meyer , Horace Fusco , Collin Smith , Alanna Hoyer-Leitzel

We develop a landscape-flux framework to investigate observed frequency distributions of vegetation and the stability of these ecological systems under fluctuations. The frequency distributions can characterize the population-potential…

Populations and Evolution · Quantitative Biology 2022-10-12 Li Xu , Denis Patterson , Ann Carla Staver , Simon Asher Levin , Jin Wang

Resiliency has garnered attention in the management of critical infrastructure as a metric of system performance, but there are significant roadblocks to its implementation in a realistic decision-making framework. Contrasted to risk and…

Systems and Control · Electrical Eng. & Systems 2026-01-08 Vincent P. Paglioni , Graeme Troxell , Aaron Brown , Steve Conrad , Mazdak Arabi

In theoretical studies, the most commonly used measure of ecological stability is resilience: ecosystems asymptotic rate of return to equilibrium after a pulse-perturbation $-$or shock. A complementary notion of growing popularity is…

Populations and Evolution · Quantitative Biology 2015-10-27 Jean-François Arnoldi , Michel Loreau , Bart Haegeman

Collectives form non-equilibrium social structures characterised by a volatile dynamics. Individuals join or leave. Social relations change quickly. Therefore, differently from engineered or ecological systems, a resilient reference state…

Physics and Society · Physics 2022-10-19 Frank Schweitzer , Christian Zingg , Giona Casiraghi

Many parts of the Earth system are thought to have multiple stable equilibrium states, with the potential for rapid and sometimes catastrophic shifts between them. The most common frameworks for analyzing stability changes, however, require…

Chaotic Dynamics · Physics 2025-07-01 Taylor Smith , Andreas Morr , Bodo Bookhagen , Niklas Boers

Extreme events represent a challenge to natural as well as man-made systems. For critical infrastructure like power grids, we need to understand their resilience against large disturbances. Recently, new measures of the resilience of…

Chaotic Dynamics · Physics 2016-06-22 Sabine Auer , Kirsten Kleis , Paul Schultz , Jürgen Kurths , Frank Hellmann

Many systems on our planet are known to shift abruptly and irreversibly from one state to another when they are forced across a "tipping point," such as mass extinctions in ecological networks, cascading failures in infrastructure systems,…

Quantitative Methods · Quantitative Biology 2022-05-23 Xueming Liu , Daqing Li , Manqing Ma , Boleslaw K. Szymanski , H Eugene Stanley , Jianxi Gao

The electric distribution system is a cornerstone of modern life, playing a critical role in the daily activities and well-being of individuals. As the world transitions toward a decarbonized future, where even mobility relies on…

Systems and Control · Electrical Eng. & Systems 2025-02-24 Shikhar Pandey , Gowtham Kandaperumal , Arslan Ahmad , Ian Dobson

Resilience is a rehashed concept in natural hazard management - resilience of cities to earthquakes, to floods, to fire, etc. In a word, a system is said to be resilient if there exists a strategy that can drive the system state back to…

Optimization and Control · Mathematics 2018-01-17 Michel De Lara

The effect of disturbance on a model ecosystem of sessile and mutually competitive species [Mathiesen et al. Phys. Rev. Lett. 107, 188101 (2011); Mitarai et al. Phys. Rev. E 86, 011929 (2012) ] is studied. The disturbance stochastically…

Populations and Evolution · Quantitative Biology 2015-06-18 Filippo Botta , Namiko Mitarai

Resilience is a rehashed concept in natural hazard management - resilience of cities to earthquakes, to floods, to fire, etc. In a word, a system is said to be resilient if there exists a strategy that can drive the system state back to…

Optimization and Control · Mathematics 2018-02-05 Michel De Lara

Natural systems are remarkably robust and resilient, maintaining essential functions despite variability, uncertainty, and hostile conditions. Understanding these nonlinear, dynamic behaviours is challenging because such systems involve…

Mathematical Physics · Physics 2025-12-02 Daniele Proverbio , Rami Katz , Giulia Giordano

We study the problem of resilient strategies in the presence of uncertainty. Resilient strategies enable an agent to make decisions that are robust against disturbances. In particular, we are interested in those disturbances that are able…

Computer Science and Game Theory · Computer Science 2026-03-02 Kush Grover , Markel Zubia , Debraj Chakraborty , Muqsit Azeem , Nils Jansen , Jan Kretinsky

Recurrence plots and their associated quantifiers provide a robust framework for detecting and characterising complex patterns in non-linear time-series. In this paper, we employ recurrence quantification analysis to investigate the…

Populations and Evolution · Quantitative Biology 2025-07-29 M. S. Palmero , M. Bongestab , N. Marwan
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