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The last decade has witnessed a surge of theoretical and computational models to describe the dynamics of complex gene regulatory networks, and how these interactions can give rise to multistable and heterogeneous cell populations. As the…

Molecular Networks · Quantitative Biology 2023-06-28 Federico Bocci , Dongya Jia , Qing Nie , Mohit Kumar Jolly , Jose Onuchic

Dynamical effects on healthy brains and brains affected by tumor are investigated via numerical simulations. The brains are modeled as multilayer networks consisting of neuronal oscillators, whose connectivities are extracted from Magnetic…

Adaptation and Self-Organizing Systems · Physics 2021-02-03 I. Koulierakis , D. A. Verganelakis , I. Omelchenko , A. Zakharova , E. Schoell , A. Provata

Self-organized network dynamics prevails for systems across physics, biology and engineering. How external signals generate distributed responses in networked systems fundamentally underlies their function, yet is far from fully understood.…

Adaptation and Self-Organizing Systems · Physics 2019-08-05 Xiaozhu Zhang , Sarah Hallerberg , Moritz Matthiae , Dirk Witthaut , Marc Timme

The activity of collections of synchronizing neurons can be represented by weakly coupled nonlinear phase oscillators satisfying Kuramoto's equations. In this article, we build such neural-oscillator models, partly based on…

Neurons and Cognition · Quantitative Biology 2012-04-27 Patrick Suppes , Jose Acacio de Barros , Gary Oas

Understanding the sensitivity of a system's behavior with respect to parameter changes is essential for many applications. This sensitivity may be desired - for instance in the brain, where a large repertoire of different dynamics,…

Dynamical Systems · Mathematics 2022-08-05 Kalel L. Rossi , Roberto C. Budzinski , Bruno R. R. Boaretto , Lyle E. Muller , Ulrike Feudel

The notion of a weak chimeras provides a tractable definition for chimera states in networks of finitely many phase oscillators. Here we generalize the definition of a weak chimera to a more general class of equivariant dynamical systems by…

Dynamical Systems · Mathematics 2017-03-01 Christian Bick

The dynamics of power-grid networks is becoming an increasingly active area of research within the physics and network science communities. The results from such studies are typically insightful and illustrative, but are often based on…

Physics and Society · Physics 2021-09-24 Takashi Nishikawa , Adilson E. Motter

In the past decade, synchronization on complex networks has attracted increasing attentions from various research disciplines. Most previous works, however, focus only on the dynamic behaviors of synchronization process in the stable…

Data Analysis, Statistics and Probability · Physics 2011-10-26 Zhao Zhuo , Shimin Cai , Jie Zhang , Zhongqian Fu

We study emergent oscillatory behavior in networks of diffusively coupled nonlinear ordinary differential equations. Starting from a situation where each isolated node possesses a globally attracting equilibrium point, we give, for an…

Dynamical Systems · Mathematics 2023-08-22 Eddie Nijholt , Tiago Pereira , Fernando C. Queiroz , Dmitry Turaev

Networks of weakly coupled oscillators had a profound impact on our understanding of complex systems. Studies on model reconstruction from data have shown prevalent contributions from hypernetworks with triplet and higher interactions among…

Dynamical Systems · Mathematics 2022-09-08 Eddie Nijholt , Jorge Luis Ocampo-Espindola , Deniz Eroglu , István Z. Kiss , Tiago Pereira

Optomechanical systems are known to exhibit a rich set of complex dynamical features including various types of chaotic behavior and multi-stability. Although this exotic behavior has attracted an intense research interest, the utilization…

Chaotic Dynamics · Physics 2021-05-19 S. Christou , V. Kovanis , A. E. Giannakopoulos , Y. Kominis

We present an interacting branching model of neural network dynamics, incorporating key biological features such as inhibition with several types of inhibitory interactions. We establish a hierarchy of analytical mean-field approximations…

Disordered Systems and Neural Networks · Physics 2025-12-29 Jeremy B. Goetz , Naruepon Weerawongphrom , Rashid V. Williams-García , John M. Beggs , Gerardo Ortiz

A large variety of rhythms are observed in nature. Rhythms such as electroencephalogram signals in the brain can often be regarded as interacting. In this study, we investigate the dynamical properties of rhythmic systems in two populations…

Chaotic Dynamics · Physics 2016-07-20 Yu Terada , Toshio Aoyagi

Little is known theoretically about the associative memory capabilities of neural networks in which information is encoded not only in the mean firing rate but also in the timing of firings. Particularly, in the case that the fraction of…

Disordered Systems and Neural Networks · Physics 2009-10-31 Toshio Aoyagi , Masaki Nomura

Analyzing synchronized nonlinear oscillators is one of the most important and attractive topics in nonlinear science. By understanding the interactions between the oscillators, we can figure out the synchronization process. A promising…

Adaptation and Self-Organizing Systems · Physics 2025-02-05 Yuka Hashimoto , Masahiro Ikeda , Hiroya Nakao , Yoshinobu Kawahara

Traditional artificial neural networks consist of nodes with non-oscillatory dynamics. Biological neural networks, on the other hand, consist of oscillatory components embedded in an oscillatory environment. Motivated by this feature of…

Neurons and Cognition · Quantitative Biology 2026-03-17 Mark A. Kramer

For large-scale power networks, the failure of particular transmission lines can offload power to other lines and cause self-protection trips to activate, instigating a cascade of line failures. In extreme cases, this can bring down the…

Physics and Society · Physics 2018-06-08 Charles Matthews , Bradly Stadie , Jonathan Weare , Mihai Anitescu , Christopher Demarco

We suggest a new perspective of research towards understanding the relations between structure and dynamics of a complex network: Can we design a network, e.g. by modifying the features of units or interactions, such that it exhibits a…

Neurons and Cognition · Quantitative Biology 2009-11-13 Raoul-Martin Memmesheimer , Marc Timme

Models of coupled oscillators are used to describe a wide variety of phenomena in neuroimaging. These models typically rest on the premise that oscillator dynamics do not evolve beyond their respective limit cycles, and hence that…

Quantitative Methods · Quantitative Biology 2019-09-19 Erik D. Fagerholm , Rosalyn J. Moran , Ines R. Violante , Robert Leech , Karl J. Friston

Randomly connected networks of excitatory and inhibitory spiking neurons provide a parsimonious model of neural variability, but are notoriously unreliable for performing computations. We show that this difficulty is overcome by…

Neurons and Cognition · Quantitative Biology 2017-01-11 Ryan Pyle , Robert Rosenbaum