相关论文: Switching in heteroclinic networks

Simple nonlinear dynamical systems with multiple stable stationary states are often taken as models for switchlike biological systems. This paper considers the interaction of multiple such simple multistable systems when they are embedded…

In this work we investigate time varying networks with complex dynamics at the nodes. We consider two scenarios of network change in an interval of time: first, we have the case where each link can change with probability pt, i.e. the…

Heteroclinic connections are trajectories that link invariant sets for an autonomous dynamical flow: these connections can robustly form networks between equilibria, for systems with flow-invariant spaces. In this paper we examine the…

Heteroclinic structures organize global features of dynamical systems. We analyze whether heteroclinic structures can arise in network dynamics with higher-order interactions which describe the nonlinear interactions between three or more…

Phase transitions in equilibrium and nonequilibrium systems play a major role in the natural sciences. In dynamical networks, phase transitions organize qualitative changes in the collective behavior of coupled dynamical units. Adaptive…

The effect of small forced symmetry breaking on the dynamics near a structurally stable heteroclinic cycle connecting two equilibria and a periodic orbit is investigated. This type of system is known to exhibit complicated, possibly chaotic…

Robust heteroclinic cycles are known to change stability in resonance bifurcations, which occur when an algebraic condition on the eigenvalues of the system is satisfied and which typically result in the creation or destruction of a…

Oscillatory dynamics are ubiquitous in biological networks. Possible sources of oscillations are well understood in low-dimensional systems, but have not been fully explored in high-dimensional networks. Here we study large networks…

Time-varying connections are crucial in understanding the structures and dynamics of complex networks. In this paper, we propose a continuous-time switching topology model for temporal networks that is driven by bursty behavior and study…

We study small white noise perturbations of planar dynamical systems with heteroclinic networks in the limit of vanishing noise. We show that the probabilities of transitions between various cells that the network tessellates the plane into…

Continuous-time systems with switch-like behaviour occur in chemical kinetics, gene regulatory networks and neural networks. Networks with hard switching, as a limiting case of smooth sigmoidal switching, retain the richest possible range…

We analyse a collection of empirical networks in a wide spectrum of disciplines and show that strong non-normality is ubiquitous in network science. Dynamical processes evolving on non-normal networks exhibit a peculiar behaviour, as…

We present a dynamical system that naturally exhibits two unstable attractors that are completely enclosed by each others basin volume. This counter-intuitive phenomenon occurs in networks of pulse-coupled oscillators with delayed…

We consider a one-dimensional network in which the nodes at Euclidean distance $l$ can have long range connections with a probabilty $P(l) \sim l^{-\delta}$ in addition to nearest neighbour connections. This system has been shown to exhibit…

Many natural systems are organized as networks, in which the nodes (be they cells, individuals or populations) interact in a time-dependent fashion. The dynamic behavior of these networks depends on how these nodes are connected, which can…

Complex network dynamics have been analyzed with models of systems of coupled switches or systems of coupled oscillators. However, many complex systems are composed of components with diverse dynamics whose interactions drive the system's…

Networks embedded in space can display all sorts of transitions when their structure is modified. The nature of these transitions (and in some cases crossovers) can differ from the usual appearance of a giant component as observed for the…

We describe a simple adaptive network of coupled chaotic maps. The network reaches a stationary state (frozen topology) for all values of the coupling parameter, although the dynamics of the maps at the nodes of the network can be…

Functional brain networks can change rapidly as a function of stimuli or cognitive shifts. Tracking dynamic functional connectivity is particularly challenging as it requires estimating the structure of the network at each moment as well as…

This article explores the relationship between communities and short cycles in complex networks, based on the fact that nodes more densely connected amongst one another are more likely to be linked through short cycles. By identifying…