English
Related papers

Related papers: Turing patterns in systems with high-order interac…

200 papers

Group classification of systems of two coupled nonlinear reaction-diffusion equation with a diagonal diffusion matrix is carried out. Symmetries of diffusion systems with singular diffusion matrix and additional first order derivative terms…

Mathematical Physics · Physics 2011-11-09 A. G. Nikitin

In his 1952 paper "The chemical basis of morphogenesis", Alan M. Turing presented a model for the formation of skin patterns. While it took several decades, the model has been validated by finding corresponding natural phenomena, e.g. in…

Neurons and Cognition · Quantitative Biology 2022-05-16 Martin Skrodzki , Ulrich Reitebuch , Eric Zimmermann

We study the evolution of networks through `triplets' - three-node graphlets. We develop a method to compute a transition matrix to describe the evolution of triplets in temporal networks. To identify the importance of higher-order…

Physics and Society · Physics 2021-08-02 Qing Yao , Bingsheng Chen , Kim Christensen , Tim S. Evans

The most fundamental social interactions among humans occur face to face. Their features have been extensively studied in recent years, owing to the availability of high-resolution data on individuals' proximity. Mathematical models based…

Physics and Society · Physics 2024-06-10 Luca Gallo , Chiara Zappalà , Fariba Karimi , Federico Battiston

When two Turing modes interact, i.e., Turing-Turing bifurcation occurs, superposition patterns revealing complex dynamical phenomena appear. In this paper, superposition patterns resulting from Turing-Turing bifurcation are investigated in…

Dynamical Systems · Mathematics 2022-04-12 Xun Cao , Weihua Jiang

Despite the tremendous advancements in the field of network theory, very few studies have taken weights in the interactions into consideration that emerge naturally in all real world systems. Using random matrix analysis of a weighted…

Physics and Society · Physics 2016-02-25 Camellia Sarkar , Sarika Jalan

In many real network systems, nodes usually cooperate with each other and form groups, in order to enhance their robustness to risks. This motivates us to study a new type of percolation, group percolation, in interdependent networks under…

Physics and Society · Physics 2018-03-21 Zexun Wang , Dong Zhou , Yanqing Hu

Higher-order interactions provide a nuanced understanding of the relational structure of complex systems beyond traditional pairwise interactions. However, higher-order network analyses also incur more cumbersome interpretations and greater…

Physics and Society · Physics 2026-01-07 Alec Kirkley , Helcio Felippe , Federico Battiston

Many networked datasets with units interacting in groups of two or more, encoded with hypergraphs, are accompanied by extra information about nodes, such as the role of an individual in a workplace. Here we show how these node attributes…

Social and Information Networks · Computer Science 2024-10-31 Anna Badalyan , Nicolò Ruggeri , Caterina De Bacco

Reaction diffusion systems with Turing instability and mass conservation are studied. In such systems, abrupt decays of stripes follow quasi-stationary states in sequence. At steady state, the distance between stripes is much longer than…

Pattern Formation and Solitons · Physics 2009-11-11 Shuji Ishihara , Mikiya Otsuji , Atsushi Mochizuki

The analysis of complex and time-evolving interactions like social dynamics represents a current challenge for the science of complex systems. Temporal networks stand as a suitable tool to schematise such systems, encoding all the appearing…

The advances in understanding complex networks have generated increasing interest in dynamical processes occurring on them. Pattern formation in activator-inhibitor systems has been studied in networks, revealing differences from the…

Adaptation and Self-Organizing Systems · Physics 2015-06-09 Nikos E. Kouvaris , Shigefumi Hata , Albert Díaz-Guilera

Spatio-temporal patterns emerging from an initial quiescent, uniform state is a phenomenon observed in many dynamical systems sustained far from thermodynamic equilibrium, the practical application of which has only recently begun to be…

Pattern Formation and Solitons · Physics 2026-02-05 Vinod Ramakrishnan , Michael J. Frazier

We performed an extensive numerical study of a two-dimensional reaction-diffusion system of the activator-inhibitor type in which domain patterns can form. We showed that both multidomain and labyrinthine patterns may form spontaneously as…

patt-sol · Physics 2016-09-08 C. B. Muratov , V. V. Osipov

Although Turing pattern is one of the most universal mechanisms for pattern formation, in its standard model the number of stripes changes with the system size, since the wavelength of the pattern is invariant: It fails to preserve the…

Cell Behavior · Quantitative Biology 2007-05-23 Shuji Ishihara , Kunihiko Kaneko

In complex systems research, the study of higher-order interactions has exploded in recent years. Researchers have formalized various types of group interactions, such as public goods games, biological contagion, and information…

Nakao and Mikhailov proposed using continuous models (mean-field models) to study reaction-diffusion systems on networks and the corresponding Turing patterns. This work aims to show that p-adic analysis is the natural tool to carry out…

Analysis of PDEs · Mathematics 2022-05-03 W. A. Zúñiga-Galindo

Empirical complex systems can be characterized not only by pairwise interactions, but also by higher-order (group) interactions influencing collective phenomena, from metabolic reactions to epidemics. Nevertheless, higher-order networks'…

Physics and Society · Physics 2026-01-01 Maxime Lucas , Luca Gallo , Arsham Ghavasieh , Federico Battiston , Manlio De Domenico

Networks are a fundamental tool for understanding and modeling complex systems in physics, biology, neuroscience, engineering, and social science. Many networks are known to exhibit rich, lower-order connectivity patterns that can be…

Social and Information Networks · Computer Science 2018-01-08 Austin R. Benson , David F. Gleich , Jure Leskovec

In the last twenty years network science has proven its strength in modelling many real-world interacting systems as generic agents, the nodes, connected by pairwise edges. Yet, in many relevant cases, interactions are not pairwise but…

Physics and Society · Physics 2020-02-26 Timoteo Carletti , Federico Battiston , Giulia Cencetti , Duccio Fanelli