Related papers: Heteroclinic Dynamics in Network Dynamical Systems…
The dynamics of networks of interacting systems depends intricately on the interaction topology. When the dynamics is explored, generally the whole topology has to be considered. However, we show that there are certain mesoscale subgraphs…
Shunting inhibitory cellular neural networks (SICNNs) with continuous as well as discontinuous external inputs are investigated. The descriptions of homoclinic and heteroclinic motions are provided in the functional sense for the…
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…
Studies of the dynamics of nonlinear recurrent neural networks often assume independent and identically distributed couplings, but large-scale connectomics data indicate that biological neural circuits exhibit markedly different…
Non-dyadic higher-order interactions affect collective behavior in various networked dynamical systems. Here we discuss the properties of a novel Ising model with higher-order interactions and characterize its phase transitions between the…
Over the last years, a great deal of attention has been focused on complex networked systems, characterized by intricate structure and dynamics. The latter has been often represented in terms of overall statistics (e.g. average and standard…
Many networks in nature and applications have an approximate low-rank structure in the sense that their connectivity structure is dominated by a few dimensions. It is natural to expect that dynamics on such networks would also be…
Hierarchically modular organization is a canonical network topology that is evolutionarily conserved in the nervous systems of animals. Within the network, neurons form directional connections defined by the growth of their axonal…
Many natural and engineered complex networks have intricate mesoscopic organization, e.g., the clustering of the constituent nodes into several communities or modules. Often, such modularity is manifested at several different hierarchical…
The propagation of traffic congestion along roads is a commonplace nonlinear phenomenon. When many roads are connected in a network, congestion can spill from one road to others as drivers queue to enter a congested road, creating further…
Topological signals, i.e., dynamical variables defined on nodes, links, triangles, etc. of higher-order networks, are attracting increasing attention. However the investigation of their collective phenomena is only at its infancy. Here we…
The understanding of neural activity patterns is fundamentally linked to an understanding of how the brain's network architecture shapes dynamical processes. Established approaches rely mostly on deviations of a given network from certain…
Time-discrete dynamical systems on a finite state space have been used with great success to model natural and engineered systems such as biological networks, social networks, and engineered control systems. They have the advantage of being…
In dynamical systems on networks, one assigns the dynamics to nodes, which are then coupled via links. This approach does not account for group interactions and dynamics on links and other higher dimensional structures. Higher-order network…
Clustering is the propensity of nodes that share a common neighbour to be connected. It is ubiquitous in many networks but poses many modelling challenges. Clustering typically manifests itself by a higher than expected frequency of…
Network structure strongly constrains the range of dynamic behaviors available to a complex system. These system dynamics can be classified based on their response to perturbations over time into two distinct regimes, ordered or chaotic,…
Although higher-order interactions are known to affect the typical state of dynamical processes giving rise to new collective behavior, how they drive the emergence of rare events and fluctuations is still an open problem. We investigate…
Traditional graph analysis focuses on nodes and edges, that is, pairwise relationships. Yet many real-world networks, including biological, social, and communication networks, involve higher-order relationships in which multiple nodes…
Experimental results often do not assess network structure; rather, the network structure is inferred by the dynamics of the nodes. From the dynamics of the nodes one then constructs a network of functional relations, termed the functional…
Representing social systems as networks, starting from the interactions between individuals, sheds light on the mechanisms governing their dynamics. However, networks encode only pairwise interactions, while most social interactions occur…