Related papers: Topological trapping in circular midpoint opinion …
We study a discrete-time consensus model in which agents iteratively update their states through interactions on a dynamic social network. At each step, a single agent is selected asynchronously and averages the values of its current…
A goal in the study of dynamics on the interval is to understand the transition to positive topological entropy. There is a conjecture from the 1980's that the only route to positive topological entropy is through a cascade of period…
Stickiness is a well known phenomenon in which chaotic orbits expend an expressive amount of time in specific regions of the chaotic sea. This phenomenon becomes important when dealing with area-preserving open systems because, in this…
The totally asymmetric simple exclusion process in discrete time is considered on finite rings with fixed number of particles. A translation-invariant version of the backward-ordered sequential update is defined for periodic boundary…
Alignment interactions in active matter are typically modeled as relaxational dynamics toward local consensus. In unbounded systems, this makes alignment effectively decoupled from local density and therefore unable to sustain self-confined…
We consider the question of determining how the topological structure influences a consensus dynamical process taking place on a network. By considering a large dataset of real-world networks we first determine that the removal of edges…
Dynamics with a threshold input--output relation commonly exist in gene, signal-transduction, and neural networks. Coupled dynamical systems of such threshold elements are investigated, in an effort to find differentiation of elements…
A central goal of protein-folding theory is to predict the stochastic dynamics of transition paths --- the rare trajectories that transit between the folded and unfolded ensembles --- using only thermodynamic information, such as a…
We study the dynamics of an asymmetric simple exclusion process with open boundaries and local interactions using a pair approximation which generalizes the 2-node cluster mean field theory and the Markov chain approach to kinetics and…
Constructing systems that exhibit time-scales much longer than those of the underlying components, as well as emergent dynamical and collective behavior, is a key goal in fields such as synthetic biology and materials self-assembly.…
Flow networks are essential for both living organisms and enginneered systems. These networks often present complex dynamics controlled, at least in part, by their topology. Previous works have shown that topologically complex networks…
Rotating the clamped ends of a buckled elastica induces a snap-through instability. Predicting the limit point and determining the equilibria at the start and end of the snap are routine computations in the quasi-static setting. The…
A stochastic process, when subject to resetting to its initial condition at a constant rate, generically reaches a non-equilibrium steady state. We study analytically how the steady state is approached in time and find an unusual relaxation…
Nonequilibrium statistical models of point vortex systems are constructed using an optimal closure method, and these models are employed to approximate the relaxation toward equilibrium of systems governed by the two-dimensional Euler…
We consider the dynamics of the disordered, one-dimensional, symmetric zero range process in which a particle from an occupied site $k$ hops to its nearest neighbour with a quenched rate $w(k)$. These rates are chosen randomly from the…
One of the fundamental structural properties of many networks is triangle closure. Whereas the influence of this transitivity on a variety of contagion dynamics has been previously explored, existing models of coevolving or adaptive network…
In this work we present novel results to the problem of the Hegselmann-Krause dynamics in networks obtained by an extensive study of the behavior of the standard order parameter sensitive to the onset of consensus: the normalized size of…
We numerically verify and analytically prove a winding number invariant that correctly predicts the number of edge states in one-dimensional, nearest-neighbor (between unit cells), two-band models with any complex couplings and open…
In this paper, we present a detailed framework to analyze the evolution of the random topology of a time-varying wireless network via the information theoretic notion of entropy rate. We consider a propagation channel varying over time with…
Trapping and un-trapping of spiral tips in a two-dimensional homogeneous excitable medium with local small-world connections is studied by numerical simulation. In a homogeneous medium which can be simulated with a lattice of regular…