Related papers: Turing instability and pattern formation on direct…
Nonreciprocity, a hallmark of nonequilibrium systems, can generate dynamics not possible near thermodynamic equilibrium, including oscillatory and rotating patterns. The onset of temporal oscillations is often evident in linearized…
Motivated by recent physics papers describing rules for natural network formation, we study an elliptic-parabolic system of partial differential equations proposed by Hu and Cai. The model describes the pressure field thanks to Darcy's type…
Pattern formation in clouds is a well-known feature, which can be observed almost every day. However, the guiding processes for structure formation are mostly unknown, and also theoretical investigations of cloud patterns are quite rare.…
Nonlinear instabilities are responsible for spontaneous pattern formation in a vast number of natural and engineered systems ranging from biology to galaxies build-up. We propose a new instability mechanism leading to pattern formation in…
Social networks play an important role in analyzing the impact of individual-level interactions on societal or economic outcomes. We model interactive decision making for a community of individuals with different traits, represented by a…
Recently, evolving networks are becoming a suitable form to model many real-world complex systems, due to their peculiarities to represent the systems and their constituting entities, the interactions between the entities and the…
We consider here the morphogenesis (pattern formation) problem for some genetic network models. First, we show that any given spatio-temporal pattern can be generated by a genetic network involving a sufficiently large number of genes.…
This paper targets at exploring how to characterize collective behaviors of directed signed networks. The right eigenvector of the Laplacian matrix associated with zero eigenvalue is further investigated and its mathematical expression is…
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.…
Inspired by the recent developments in modeling and analysis of reaction networks, we provide a geometric formulation of the reversible reaction networks under the influence of diffusion. Using the graph knowledge of the underlying reaction…
Communities in directed networks have often been characterized as regions with a high density of links, or as sets of nodes with certain patterns of connection. Our approach for community detection combines the optimization of a quality…
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…
Understanding how local perturbations induce the transient dynamics of a network of coupled units is essential to control and operate such systems. Often a perturbation initiated in one unit spreads to other units whose dynamical state they…
The study of the dynamics of chemical reactions, and in particular phenomena such as oscillating reactions, has led to the recognition that many dynamical properties of a chemical reaction can be predicted from graph theoretical properties…
Turing instability in complex networks have been shown in the literature to be dominated by the distribution of the nodal degrees. The conditions for Turing instability have been derived with an explicit dependence on the eigenvalues of the…
Large-scale recurrent networks have drawn increasing attention recently because of their capabilities in modeling a large variety of real-world phenomena and physical mechanisms. This paper studies how to identify all authentic connections…
This paper presents an algebraic framework to study sign-sensitivities for reaction networks modeled by means of systems of ordinary differential equations. Specifically, we study the sign of the derivative of the concentrations of the…
We propose an adaptive control protocol for identifying the topology of dynamical networks interconnected over undirected graphs with cooperative and antagonistic interactions. The signed network is modeled using a repelling Laplacian.…
Topology learning of networked dynamical systems is an important problem with implications to optimal control, decision-making over networks, cybersecurity and safety. The majority of prior work in consistent topology estimation relies on…
A general system of several ordinary differential equations coupled with a reaction-diffusion equation in a bounded domain with zero-flux boundary condition is studied in the context of pattern formation. These initial-boundary value…