Related papers: A mathematical framework for critical transitions:…
Noise plays a fundamental role in a wide variety of physical and biological dynamical systems. It can arise from an external forcing or due to random dynamics internal to the system. It is well established that even weak noise can result in…
Statistical systems near a classical critical point have been intensively studied both from theoretical and experimental points of view. In particular, correlation functions are of relevance in comparing theoretical models with the…
Random graphs have played an instrumental role in modelling real-world networks arising from the internet topology, social networks, or even protein-interaction networks within cells. Percolation, on the other hand, has been the fundamental…
Predicting critical transitions in complex systems, such as epileptic seizures in the brain, represents a major challenge in scientific research. The high-dimensional characteristics and hidden critical signals further complicate…
Critical transitions and tipping phenomena between two meta-stable states in stochastic dynamical systems are a significant scientific issue. In this work, we expand the methodology of identifying the most probable transition pathway…
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,…
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…
We study the ABC model (A + B --> 2B, B + C --> 2C, C + A --> 2A), and its counterpart: the three--component neutral drift model (A + B --> 2A or 2B, B + C --> 2B or 2C, C + A --> 2C or 2A.) In the former case, the mean field approximation…
Second-order phase transitions are characterised by critical scaling and universality. The singular behaviour of thermodynamic quantities at the transition, in particular, is determined by critical exponents of the universality class of the…
We report the discovery of a discrete hierarchy of micro-transitions occurring in models of continuous and discontinuous percolation. The precursory micro-transitions allow us to target almost deterministically the location of the…
Experimental systems with a first order phase transition will often exhibit hysteresis when out of equilibrium. If defects are present, the hysteresis loop can have different shapes: with small disorder the hysteresis loop has a macroscopic…
We perform both analytical and numerical bifurcation analysis of a forest-grassland ecosystem model coupled with human interaction. The model consists of two nonlinear ordinary differential equations incorporating the human perception of…
A classification of critical behavior is provided in systems for which the renormalization group equations are control-parameter dependent. It describes phase transitions in networks with a recursive, hierarchical structure but appears to…
Highly-diverse ecosystems exhibit a broad distribution of population sizes and species turnover, where species at high and low abundances are exchanged over time. We show that these two features generically emerge in the fluctuating phase…
These lectures focus on bifurcation analysis as a tool for studying phase transitions that occur in models of liquid-crystalline systems. We show how this approach bridges the gap between the phenomenological Landau theory and the --- often…
We analyse how the sampling dynamics of distributions evolve in score-based diffusion models using cross-fluctuations, a centered-moment statistic from statistical physics. Specifically, we show that starting from an unbiased isotropic…
In a nonautonomous nonlinear dynamical system, generic critical transitions (tipping points) are not limited to slow passage through fold bifurcations. They can also correspond to slow passage through other generic bifurcations, such as…
We extend the theory of quasipotentials in dynamical systems by calculating, within a broad class of period-doubling maps, an exact potential for the critical fluctuations of pitchfork bifurcations in the weak noise limit. These…
A general method to describe a second-order phase transition is discussed. It starts from the energy level statistics and uses of finite-size scaling. It is applied to the metal-insulator transition (MIT) in the Anderson model of…
Ecological and evolutionary processes show various population dynamics depending on internal interactions and environmental changes. While crucial in predicting biological processes, discovering general relations for such nonlinear dynamics…