# Networks

# Stationary patterns in star networks of bistable units: Theory and application to chemical reactions

We present theoretical and experimental studies on pattern formation with bistable dynamical units coupled in a star network configuration. By applying a localized perturbation to the central or the peripheral elements, we demonstrate the subsequent spreading, pinning, or retraction of

# Stationary patterns in star networks of bistable units: Theory and application to chemical reactions

We present theoretical and experimental studies on pattern formation with bistable dynamical units coupled in a star network configuration. By applying a localized perturbation to the central or the peripheral elements, we demonstrate the subsequent spreading, pinning, or retraction of

# Chimera states in network-organized public goods games with destructive agents

It is shown that a network-organized metapopulation of cooperators, defectors and destructive agents playing the public goods game with mutations, can collectively reach global synchronization or chimera states. Global synchronization is accompanied by a collective periodic burst of cooperation, whereas

# Chimera states in network-organized public goods games with destructive agents

It is shown that a network-organized metapopulation of cooperators, defectors and destructive agents playing the public goods game with mutations, can collectively reach global synchronization or chimera states. Global synchronization is accompanied by a collective periodic burst of cooperation, whereas

# Self-Organized Stationary Patterns in Networks of Bistable Chemical Reactions

Experiments with networks of discrete reactive bistable electrochemical elements organized in regular and nonregular tree networks are presented to confirm an alternative to the Turing mechanism for the formation of self-organized stationary patterns. The results show that the pattern formation

# Self-Organized Stationary Patterns in Networks of Bistable Chemical Reactions

Experiments with networks of discrete reactive bistable electrochemical elements organized in regular and nonregular tree networks are presented to confirm an alternative to the Turing mechanism for the formation of self-organized stationary patterns. The results show that the pattern formation

# Chimera-like states in modular networks

Inspired by the ancient Greek mythological creature Chimera (χίμαιρα) which had a lion’s head, a goat’s body and a serpent’s tail, Abrams and Strogatz [1] coined the term “chimera states” for the counterintuitive self-organized phenomenon in which synchronous and desynchronous

# Chimera-like states in modular networks

Inspired by the ancient Greek mythological creature Chimera (χίμαιρα) which had a lion’s head, a goat’s body and a serpent’s tail, Abrams and Strogatz [1] coined the term “chimera states” for the counterintuitive self-organized phenomenon in which synchronous and desynchronous

# Tutorial 5 for WWCS2016

IPython Notebooks for the Tutorial 5 of the Winter Workshop on Complex Systems 2016 This python notebook solves a bistable system on a complex network and visualizes the solution Import networkx library import networkx as nx For the numerical integration

# Tutorial 5 for WWCS2016

IPython Notebooks for the Tutorial 5 of the Winter Workshop on Complex Systems 2016 This python notebook solves a bistable system on a complex network and visualizes the solution Import networkx library import networkx as nx For the numerical integration

# multiNetX v1.0

multiNetX is a python package for the manipulation and visualization of multilayer networks. The core of this package is a MultilayerGraph, a class that inherits all the features of networkx.Graph(). multiNetX inheriths all features from NetworkX Features: Creating networks with

# multiNetX v1.0

multiNetX is a python package for the manipulation and visualization of multilayer networks. The core of this package is a MultilayerGraph, a class that inherits all the features of networkx.Graph(). multiNetX inheriths all features from NetworkX Features: Creating networks with

# Feedback induced patterns in bistable networks

Effects of feedbacks on self-organization phenomena in networks of diffusively coupled bistable elements are investigated. For regular trees, an approximate analytical theory for localized stationary patterns under application of global feedbacks is constructed. Using it, properties of such patterns in

# Feedback induced patterns in bistable networks

Effects of feedbacks on self-organization phenomena in networks of diffusively coupled bistable elements are investigated. For regular trees, an approximate analytical theory for localized stationary patterns under application of global feedbacks is constructed. Using it, properties of such patterns in

# Excitable networks

Excitation waves are studied on trees and random networks of coupled active elements. Undamped propagation of such waves is observed in those networks. It represents an excursion from the resting state and a relaxation back to it for each node.

# Excitable networks

Excitation waves are studied on trees and random networks of coupled active elements. Undamped propagation of such waves is observed in those networks. It represents an excursion from the resting state and a relaxation back to it for each node.

# Bistable tree networks: Traveling and pinned fronts

Traveling fronts and stationary localized patterns in bistable reaction-diffusion systems have been broadly studied for classical continuous media and regular lattices. Analogs of such non-equilibrium patterns are also possible in networks. Here, we consider traveling and stationary patterns in bistable

# Bistable tree networks: Traveling and pinned fronts

Traveling fronts and stationary localized patterns in bistable reaction-diffusion systems have been broadly studied for classical continuous media and regular lattices. Analogs of such non-equilibrium patterns are also possible in networks. Here, we consider traveling and stationary patterns in bistable

# Pattern formation in multiplex networks

We study pattern formation in the new framework of multiplex networks, where activator and inhibitor species occupy separate nodes in different layers. Species react across layers but diffuse only within their own layer of distinct network topology. This multiplicity generates

# Pattern formation in multiplex networks

We study pattern formation in the new framework of multiplex networks, where activator and inhibitor species occupy separate nodes in different layers. Species react across layers but diffuse only within their own layer of distinct network topology. This multiplicity generates