Related papers: Pattern reconstruction through generalized eigenve…
In this paper, the Turing instability in reaction-diffusion models defined on complex networks is studied. Here, we focus on three types of models which generate complex networks, i.e. the Erd\H{o}s-R\'enyi, the Watts-Strogatz, and the…
Adaptive transport networks in biological and physical systems exhibit hierarchical organization, characteristic channel spacing, and robust scaling relations. Existing adaptive network models, formulated on a lattice, successfully…
Transport is an important function in many network systems and understanding its behavior on biological, social, and technological networks is crucial for a wide range of applications. However, it is a property that is not well-understood…
Recurrently coupled oscillators that are sufficiently heterogeneous and/or randomly coupled can show an asynchronous activity in which there are no significant correlations among the units of the network. The asynchronous state can…
We study the network reconstruction problem for an epidemic reaction-diffusion. These models are an extension of deterministic, compartmental models to a graph setting, where the reactions within the nodes are coupled by a diffusion. We…
Symmetries naturally occur in real-world networks and can significantly influence the observed dynamics. For instance, many synchronization patterns result from the underlying network symmetries, and high symmetries are known to increase…
Robustness to perturbation is a key topic in the study of complex systems occurring across a wide variety of applications from epidemiology to biochemistry. Here we analyze the eigenspectrum of the Jacobian matrices associated to a general…
The problem of Turing pattern formation has attracted much attention in nonlinear science as well as physics, chemistry and biology. So far all Turing patterns have been observed in stationary and oscillatory media only. In this letter we…
This paper investigates the conditions for the stability and emergence of patterns in a new three-component reaction-diffusion system. The system describes the coexistence and interaction of water reservoirs, vegetation, and bushfire…
Recent experiments have exploited elastic instabilities in membranes to create complex patterns. However, the rational design of such structures poses many challenges, as they are products of nonlinear elastic behavior. We pose a simple…
A thermodynamically motivated neural network model is described that self-organizes to transport charge associated with internal and external potentials while in contact with a thermal reservoir. The model integrates techniques for rapid,…
From the perspective of network analysis, the ubiquitous networks are comprised of regular and irregular components, which makes uncovering the complexity of network structures to be a fundamental challenge. Exploring the regular…
Fully developed turbulence is a universal and scale-invariant chaotic state characterized by an energy cascade from large to small scales where the cascade is eventually arrested by dissipation. In this article, we show how to harness these…
Here we propose a generic mechanism - networked buffering - for generating robust traits in complex systems that requires two basic conditions to be satisfied: 1) agents are versatile enough to perform more than one single functional role…
This letter seeks to illuminate the profound connection between complexity, self-organization, emergent behaviour, pattern formation, and entropy concepts that are foundational to understanding our universe. By examining these ideas through…
Turing's mechanism is often invoked to explain periodic patterns in nature, although direct experimental support is scarce. Turing patterns form in reaction-diffusion systems when the activating species diffuse much slower than the…
Characterizing the emergence of chaotic dynamics of complex networks is an essential task in nonlinear science with potential important applications in many fields such as neural control engineering, microgrid technologies, and ecological…
The network of interactions in complex systems, strongly influences their resilience, the system capability to resist to external perturbations or structural damages and to promptly recover thereafter. The phenomenon manifests itself in…
We study an ensemble of random walkers carrying internal noisy phase oscillators which are synchronized among the walkers by local interactions. Due to individual mobility, the interaction partners of every walker change randomly, hereby…
The transition to turbulence via spatiotemporal intermittency is investigated in the context of coupled maps defined on small-world networks. The local dynamics is given by the Chat\'e-Manneville minimal map previously used in studies of…