Related papers: Switching in heteroclinic networks
The characterization of the "most connected" nodes in static or slowly evolving complex networks has helped in understanding and predicting the behavior of social, biological, and technological networked systems, including their robustness…
Many natural systems, such as neurons firing in the brain or basketball teams traversing a court, give rise to time series data with complex, nonlinear dynamics. We can gain insight into these systems by decomposing the data into segments…
In this article the generalized Lotka-Volterra model of ensemble of four excitory or inhibitory coupled elements are studied. It is shown that in the phase space of the model there exist heteroclinic network: a connected union of two or…
Many real-world complex networks contain a significant amount of structural redundancy, in which multiple vertices play identical topological roles. Such redundancy arises naturally from the simple growth processes which form and shape many…
We study the structural characteristics of complex networks using the representative eigenvectors of the adjacent matrix. The probability distribution function of the components of the representative eigenvectors are proposed to describe…
In discrete-time dynamics, it is frequently assumed that the transition probabilities (e.g., the recovery probability) are independent of the network structure. However, there is a lack of empirical evidence to support this claim in large…
Complex networks are frequently employed to model physical or virtual complex systems. When certain entities exist across multiple systems simultaneously, unveiling their corresponding relationships across the networks becomes crucial. This…
We consider a general model in which there is a coupled dynamics of node states and links states in a network. This coupled dynamics coevolves with dynamical changes of the topology of the network caused by a link rewiring mechanism. Such…
A network with local dynamics of logistic type is considered. We implement a mean-field multiplicative coupling among first-neighbor nodes. When the coupling parameter is small the dynamics is dissipated and there is no activity: the…
We propose a statistical model of a large random network with high connectivity in order to describe the behavior of {\it E.\,coli} cells after exposure to acute stress. The building blocks of this network are feedback cycles typical of the…
We perform experiments and phase model simulations with a ring network of oscillatory electrochemical reactions to explore the effect of random connections and non-isochronocity of the interactions on the pattern formation. A few additional…
We explore the coupled dynamics of the internal states of a set of interacting elements and the network of interactions among them. Interactions are modeled by a spatial game and the network of interaction links evolves adapting to the…
We first recall several historical oscillating bridges that, in some cases, led to collapses. Some of them are quite recent and show that, nowadays, oscillations in suspension bridges are not yet well understood. Next, we survey some…
The phenomenon of slow switching in populations of globally coupled oscillators is discussed. This characteristic collective dynamics, which was first discovered in a particular class of the phase oscillator model, is a result of the…
Over the past two decades, complex network theory provided the ideal framework for investigating the intimate relationships between the topological properties characterizing the wiring of connections among a system's unitary components and…
Plane Couette flow transitions to turbulence for Re~325 even though the laminar solution with a linear profile is linearly stable for all Re (Reynolds number). One starting point for understanding this subcritical transition is the…
Network modeling based on ensemble averages tacitly assumes that the networks meant to be modeled are typical in the ensemble. Previous research on network eigenvalues, which govern a range of dynamical phenomena, has shown that this is…
The interplay between time scales and structural properties of complex networks of nonlinear oscillators can generate many interesting phenomena, like amplitude death, cluster synchronization, frequency synchronization etc. We study the…
We consider a white noise perturbation of dynamics in the neighborhood of a heteroclinic network. We show that under the logarithmic time rescaling the diffusion converges in distributon in a special topology to a piecewise constant process…
Interdependent networks are characterized by two kinds of interactions: The usual connectivity links within each network and the dependency links coupling nodes of different networks. Due to the latter links such networks are known to…