Extreme events in dynamical systems and random walkers: A review

Abstract

Extreme events gain the attention of researchers due to their utmost importance in various contexts ranging from finance to climatology. This brings such recurrent events to the limelight of attention in interdisciplinary research. A comprehensive review of recent progress is provided to capture recent improvements in analyzing such very high-amplitude events from the point of view of dynamical systems and random walkers. We emphasize, in detail, the mechanisms responsible for the emergence of such events in complex systems. Several mechanisms that contribute to the occurrence of extreme events have been elaborated that investigate the sources of instabilities leading to them. In addition, we discuss the prediction of extreme events from two different contexts, using dynamical instabilities and data-based machine learning algorithms. Tracking of instabilities in the phase space is not always feasible and precise knowledge of the dynamics of extreme events does not necessarily help in forecasting extreme events. Moreover, in most studies on high-dimensional systems, only a few degrees of freedom participate in extreme events' formation. Thus, the notable inclusion of prediction through machine learning is of enormous significance, particularly for those cases where the governing equations of the model are explicitly unavailable. Besides, random walks on complex networks can represent several transport processes, and exceedances of the flux of walkers above a prescribed threshold may describe extreme events. We unveil the theoretical studies on random walkers with their enormous potential for applications in reducing extreme events. We cover the possible controlling strategies, which may be helpful to mitigate extreme events in physical situations like traffic jams, heavy load of web requests, competition for shared resources, floods in the network of rivers, and many more.

78 pages, 30 figures Accepted for publication in Physics Reports on 6th April 2022

References in corpus (55)

• Deep Learning in Neural Networks: An Overview
• Synchronization in complex networks
• Statistical physics of human cooperation
• Diffusion dynamics on multiplex networks
• Chimera states: Coexistence of coherence and incoherence in networks of coupled oscillators
• Social diversity and promotion of cooperation in the spatial prisoner's dilemma game
• Reward and cooperation in the spatial public goods game
• Synchronous bursts on scale-free neuronal networks with attractive and repulsive coupling
• Heterogeneous aspirations promote cooperation in the prisoner's dilemma game
• Dragon-kings: mechanisms, statistical methods and empirical evidence
• Dynamics of jamming transitions in complex networks
• Chimera states in a multilayer network of coupled and uncoupled neurons
• Chimera states in uncoupled neurons induced by a multilayer structure
• An approach to chaotic synchronization
• Recurrence time analysis, long-term correlations, and extreme events
• The synchronized dynamics of time-varying networks
• Chimera states: Effects of different coupling topologies
• Congestion phenomena on complex networks
• Extreme multistability: Attractor manipulation and robustness
• The entropic origin of disassortativity in complex networks
• Generalized synchronization: a modified system approach
• Generalized synchronization of chaos for secure communication: remarkable stability to noise
• Return interval distribution of extreme events and long term memory
• Extreme events on complex networks
• Route to extreme events in excitable systems
• Swarmalators under competitive time-varying phase interactions
• Complex network based techniques to identify extreme events and (sudden) transitions in spatio-temporal systems
• Machine learning algorithms for predicting the amplitude of chaotic laser pulses
• Density of near-extreme events
• Eco-evolutionary dynamics of cooperation in the presence of policing
• Intermittent large deviation of chaotic trajectory in Ikeda map: Signature of extreme events
• Distance dependent competitive interactions in a frustrated network of mobile agents
• Extreme events in globally coupled chaotic maps
• Perspective on attractive-repulsive interactions in dynamical networks: progress and future
• Synchronization of moving oscillators in three dimensional space
• Effect of repulsive links on frustration in attractively coupled networks
• Understanding the origin of extreme events in El Niño-Southern Oscillation
• Probabilistic response and rare events in Mathieu's equation under correlated parametric excitation
• Survivability of a metapopulation under local extinctions
• Optimized ensemble deep learning framework for scalable forecasting of dynamics containing extreme events
• Spreading dynamics on spatially constrained complex brain networks
• Coherent libration to coherent rotational dynamics via chimeralike states and clustering in Josephson Junction array
• Using Machine Learning to predict extreme events in the Hénon map
• Record statistics of financial time series and geometric random walks
• Predictability of Extreme Intensity Pulses in Optically Injected Semiconductor Lasers
• Model-free prediction of emergence of extreme events in a parametrically driven nonlinear dynamical system by Deep Learning
• Emergent rhythms in coupled nonlinear oscillators due to dynamic interactions
• Instabilities in quasiperiodic motion lead to intermittent large-intensity events in Zeeman laser
• Emergence and mitigation of extreme events in a parametrically driven system with velocity-dependent potential
• Identifying edges that facilitate the generation of extreme events in networked dynamical systems
• Early warning signal for interior crises in excitable systems
• Symmetrical emergence of extreme events at multiple regions in a damped and driven velocity-dependent mechanical system
• Amplitude mediated spiral chimera pattern in a nonlinear reaction-diffusion system
• Prediction of Occurrence of Extreme Events using Machine Learning
• Random Walks on Complex Networks

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• The synchronized dynamics of time-varying networks
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• Transition to hyperchaos: Sudden expansion of attractor and intermittent large-amplitude events in dynamical systems
• Extreme events in a complex network: interplay between degree distribution and repulsive interaction
• Extreme bursting events via pulse-shaped explosion in mixed Rayleigh-Lienard nonlinear oscillator
• Instabilities in quasiperiodic motion lead to intermittent large-intensity events in Zeeman laser
• Emergence of extreme events in a quasi-periodic oscillator
• Interlayer antisynchronization in degree-biased duplex networks
• Extreme rotational events in a forced-damped nonlinear pendulum
• Challenges and perspectives in recurrence analyses of event time series
• Detection and Forecasting of Extreme event in Stock Price Triggered by Fundamental, Technical, and External Factors
• Noise-induced Extreme Events in Hodgkin-Huxley Neural Networks
• Propagation of extreme events in multiplex neuronal networks
• Heterogeneous noise-induced extreme events and synchronization in a globally coupled network of FitzHugh-Nagumo oscillators
• Extreme events in the Lienard system with asymmetric potential: An in-depth exploration
• Smart Walkers in Discrete Space