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Nonlinear dynamics can give rise, via the processes of self-organisation and pattern formation, to the spontaneous manifestation of order in open and complex systems far from equilibrium. Self-organising systems, transforming the inflow of…

Materials Science · Physics 2023-05-03 M. Gidding , T. Janssen , C. S. Davies , A. Kirilyuk

Symmetry-breaking instabilities play an important role in understanding the mechanisms underlying the diversity of patterns observed in nature, such as in Turing's reaction--diffusion theory, which connects cellular signalling and transport…

Pattern Formation and Solitons · Physics 2023-12-25 Andrew L. Krause , Eamonn A. Gaffney , Thomas Jun Jewell , Václav Klika , Benjamin J. Walker

As a model of temporally evolving networks, we consider a globally coupled logistic map with variable connection weights. The model exhibits self-organization of network structure, reflected by the collective behavior of units. Structural…

Disordered Systems and Neural Networks · Physics 2009-11-07 Junji Ito , Kunihiko Kaneko

Large networks of spiking neurons show abrupt changes in their collective dynamics resembling phase transitions studied in statistical physics. An example of this phenomenon is the transition from irregular, noise-driven dynamics to…

Adaptation and Self-Organizing Systems · Physics 2008-11-25 Vicenç Gómez , Andreas Kaltenbrunner , Vicente López , Hilbert J. Kappen

Despite their apparent diversity, modern machine learning methods can be reduced to a remarkably simple core principle: learning is achieved by continuously optimizing parameters to minimize or maximize a scalar objective function. This…

Machine Learning · Computer Science 2026-02-24 Sheng Ran

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…

Analysis of PDEs · Mathematics 2019-08-06 Eric Forgoston , Richard O. Moore

Transitions from turbulence to order are studied experimentally in thin fluid layers and magnetically confined toroidal plasma. It is shown that turbulence self-organizes through the mechanism of spectral condensation. The spectral…

Plasma Physics · Physics 2009-11-10 M. G. Shats , H. Xia , H. Punzmann

The cohesive collective motion (flocking, swarming) of autonomous agents is ubiquitously observed and exploited in both natural and man-made settings, thus, minimal models for its description are essential. In a model with continuous space…

Statistical Mechanics · Physics 2015-01-12 Illes J. Farkas , Jeromos Kun , Yi Jin , Gaoqi He , Mingliang Xu

Improving traffic management in case of perturbation is one of the main challenges in today's railway research. The great majority of the existing literature proposes approaches to make centralized decisions to minimize delay propagation.…

Computers and Society · Computer Science 2026-04-21 Federico Naldini , Fabio Oddi , Leo D'Amato , Grégory Marlière , Vito Trianni , Paola Pellegrini

Power laws and distributions with heavy tails are common features of many experimentally studied complex systems, like the distribution of the sizes of earthquakes and solar flares, or the duration of neuronal avalanches in the brain.…

Adaptation and Self-Organizing Systems · Physics 2014-03-05 Dimitrije Markovic , Claudius Gros

The emergence of global order in complex systems with locally interacting components is most striking at criticality, where small changes in control parameters result in a sudden global re-organization. We introduce a measure of…

Statistical Mechanics · Physics 2020-10-02 Ramil Nigmatullin , Mikhail Prokopenko

The Self-Optimization (SO) model is a useful computational model for investigating self-organization in "soft" Artificial life (ALife) as it has been shown to be general enough to model various complex adaptive systems. So far, existing…

Adaptation and Self-Organizing Systems · Physics 2023-04-07 Natalya Weber , Werner Koch , Tom Froese

Equilibrium is a rather ideal situation, the exception rather than the rule in Nature. Whenever the external or internal parameters of a physical system are varied its subsequent relaxation to equilibrium may be either impossible or take…

Statistical Mechanics · Physics 2016-10-04 Leticia F. Cugliandolo

We present a general framework for modeling a wide selection of flocking scenarios under free boundary conditions. Several variants have been considered - including examples for the widely observed behavior of hierarchically interacting…

Physics and Society · Physics 2019-04-23 Yongnan Jia , Tamas Vicsek

We present a fluid-dynamic model for the simulation of urban traffic networks with road sections of different lengths and capacities. The model allows one to efficiently simulate the transitions between free and congested traffic, taking…

Popular Physics · Physics 2007-05-23 Dirk Helbing , Stefan Lämmer , Jean-Patrick Lebacque

A population of heterogenous agents compeeting through a minority rule is investigated. Agents which frequently loose are selected for evolution by changing their strategies. The stationary composition of the population resulting for this…

Disordered Systems and Neural Networks · Physics 2009-10-31 Alexei Vazquez

Emergence of self-similarity in hierarchical community structures is ubiquitous in complex systems. Yet, there is a dearth of universal quantification and general principles describing the formation of such structures. Here, we discover…

Physics and Society · Physics 2025-07-16 Shruti Tandon , Nidhi Dilip Sonwane , Tobias Braun , Norbert Marwan , Juergen Kurths , R. I. Sujith

Self-organization is a process where order of a whole system arises out of local interactions between small components of a system. Emergy, spelled with an 'm', defined as the amount of (solar) energy used to make a product or service, is…

Formal Languages and Automata Theory · Computer Science 2019-06-26 Chams Lahlou , Laurent Truffet

A hallmark of living systems is the ability to employ a common set of versatile building blocks that can self-organize into a multitude of different structures, in a way that can be controlled with minimal cost. This capability can only be…

Statistical Mechanics · Physics 2022-01-26 Saeed Osat , Ramin Golestanian

Modeling human operator's dynamic plays a very important role in the manual closed-loop control system, and it is an active research area for several decades. Based on the characteristics of human brain and behaviour, a new kind of…

Systems and Control · Computer Science 2016-01-11 Jiacai Huang , Yangquan Chen , Haibin Li , Xinxin Shi