Related papers: Catastrophic Phase Transitions and Early Warnings …
Catastrophic transitions, where a system shifts abruptly between alternate steady states, are a generic feature of many nonlinear systems. Recently these regime shift were suggested as the mechanism underlies many ecological catastrophes,…
Ecosystems often undergo abrupt regime shifts in response to gradual external changes. These shifts are theoretically understood as a regime switch between alternative stable states of the ecosystem dynamical response to smooth changes in…
Summary 1. Infectious disease outbreaks in plants threaten ecosystems, agricultural crops and food trade. Currently, several fungal diseases are affecting forests worldwide, posing a major risk to tree species, habitats and consequently…
Ecosystems display a complex spatial organization. Ecologists have long tried to characterize them by looking at how different measures of biodiversity change across spatial scales. Ecological neutral theory has provided simple predictions…
Social ecological systems are often difficult to investigate and manage because of their inherent complexity1. Small variations in external drivers can lead to abrupt changes associated with instabilities and bifurcations in the underlying…
The early prediction of tipping points, distinguished by sudden and catastrophic shifts from stable states, poses a challenging task that would enable us to assess the impending threat across natural and engineered systems. This threat…
A large variety of complex systems in ecology, climate science, biomedicine and engineering have been observed to exhibit tipping points, where the internal dynamical state of the system abruptly changes. For example, such critical…
Critical transitions, or large changes in the state of a system after a small change in the system's external conditions or parameters, commonly occur in a wide variety of disciplines, from the biological and social sciences to physics.…
Dryland vegetation ecosystems are known to be susceptible to critical transitions between alternative stable states when subjected to external forcing. Such transitions are often discussed through the framework of bifurcation theory, but…
In this paper, we focus on the influence of heterogeneity and stochasticity of the population on the dynamical structure of a basic susceptible-infected-susceptible (SIS) model. First we prove that, upon a suitable mathematical…
Spatial patterns are widely observed in numerous nonequilibrium natural systems, often undergoing complex transitions and bifurcations, thereby exhibiting significant importance in many physical and biological systems such as embryonic…
The presence of one or more species at some spatial locations but not others is a central matter in ecology. This phenomenon is related to ecological pattern formation. Nonlocal interactions can be considered as one of the mechanisms…
The theory of alternative stable states and tipping points has garnered substantial attention in the last several decades. It predicts potential critical transitions from one ecosystem state to a completely different state under increasing…
The potential for complex systems to exhibit tipping points in which an equilibrium state undergoes a sudden and often irreversible shift is well established, but prediction of these events using standard forecast modeling techniques is…
Current early warning signs for tipping points often fail to distinguish between catastrophic shifts and less dramatic state changes, such as spatial pattern formation. This paper introduces a novel method that addresses this limitation by…
Detecting early warning indicators for abrupt dynamical transitions in complex systems or high-dimensional observation data is essential in many real-world applications, such as brain diseases, natural disasters, and engineering…
Spatial extent is a complicating factor in mathematical biology. The possibility that an action at point A cannot immediately affect what happens at point B creates the opportunity for spatial nonuniformity. This nonuniformity must change…
The realization that complex systems such as ecological communities can collapse or shift regimes suddenly and without rapid external forcing poses a serious challenge to our understanding and management of the natural world. The potential…
Spatial systems with heterogeneities are ubiquitous in nature, from precipitation, temperature and soil gradients controlling vegetation growth to morphogen gradients controlling gene expression in embryos. Such systems, generally described…
Understanding how species persist under interacting stressors is a central challenge in ecology. We develop a spatially explicit reaction-diffusion framework to investigate competing species in landscapes shaped by climate variability,…