Related papers: Nonlinear network dynamics under perturbations of …
Recent studies have been using graph theoretical approaches to model complex networks (such as social, infrastructural or biological networks), and how their hardwired circuitry relates to their dynamic evolution in time. Understanding how…
A great variety of systems in nature, society and technology -- from the web of sexual contacts to the Internet, from the nervous system to power grids -- can be modeled as graphs of vertices coupled by edges. The network structure,…
We explore the interplay of network structure, topology, and dynamic interactions between nodes using the paradigm of distributed synchronization in a network of coupled oscillators. As the network evolves to a global steady state,…
We study the temporal co-variation of network co-evolution via the cross-link structure of networks, for which we take advantage of the formalism of hypergraphs to map cross-link structures back to network nodes. We investigate two sets of…
I briefly survey several fascinating topics in networks and nonlinearity. I highlight a few methods and ideas, including several of personal interest, that I anticipate to be especially important during the next several years. These topics…
To find interesting structure in networks, community detection algorithms have to take into account not only the network topology, but also dynamics of interactions between nodes. We investigate this claim using the paradigm of…
There is enormous interest -- both mathematically and in diverse applications -- in understanding the dynamics of coupled oscillator networks. The real-world motivation of such networks arises from studies of the brain, the heart, ecology,…
Recent experimental advances are producing an avalanche of data on both neural connectivity and neural activity. To take full advantage of these two emerging datasets we need a framework that links them, revealing how collective neural…
In a complex system, the interactions between individual agents often lead to emergent collective behavior like spontaneous synchronization, swarming, and pattern formation. The topology of the network of interactions can have a dramatic…
Complexity in the temporal organization of neural systems may be a reflection of the diversity of its neural constituents. These constituents, excitatory and inhibitory neurons, comprise an invariant ratio in vivo and form the substrate for…
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…
Recurrent Neural Network models have elucidated the interplay between structure and dynamics in biological neural networks, particularly the emergence of irregular and rhythmic activities in cortex. However, most studies have focused on…
In this work, we investigate a model of an adaptive networked dynamical system, where the coupling strengths among phase oscillators coevolve with the phase states. It is shown that in this model the oscillators can spontaneously…
The paper examines the discrete-time dynamics of neuron models (of excitatory and inhibitory types) with piecewise linear activation functions, which are connected in a network. The properties of a pair of neurons (one excitatory and the…
Biological rhythms are generated by pacemaker organs, such as the heart pacemaker organ (the sinoatrial node) and the master clock of the circadian rhythms (the suprachiasmatic nucleus), which are composed of a network of autonomously…
Many natural systems are organized as networks, in which the nodes interact in a time-dependent fashion. The object of our study is to relate connectivity to the temporal behavior of a network in which the nodes are (real or complex)…
The relation between network structure and dynamics is determinant for the behavior of complex systems in numerous domains. An important long-standing problem concerns the properties of the networks that optimize the dynamics with respect…
Correlated fluctuations in the activity of neural populations reflect the network's dynamics and connectivity. The temporal and spatial dimensions of neural correlations are interdependent. However, prior theoretical work mainly analyzed…
Recent work in modeling the coupling between disease dynamics and dynamic social network geometry has led to the examination of how human interactions force a rewiring of connections in a population. Rewiring of the network may be…
Networks of coupled phase oscillators are one of the most studied dynamical systems with numerous applications in physics, chemistry, biology, and engineering. Their behaviour is often characterized by the emergence of various partially…