Related papers: Phase-locking in weakly heterogeneous neuronal net…
Realistic large-scale networks display an heterogeneous distribution of connectivity weights, that might also randomly vary in time. We show that depending on the level of heterogeneity in the connectivity coefficients, different…
We study the evolution of heterogeneous networks of oscillators subject to a state-dependent interconnection rule. We find that heterogeneity in the node dynamics is key in organizing the architecture of the functional emerging networks. We…
This article studies stochastic relative phase stability, i.e., stochastic phase-cohesiveness, of discrete-time phase-coupled oscillators. Stochastic phase-cohesiveness in two types of networks is studied. First, we consider oscillators…
Synchronized oscillations in networks of inhibitory and excitatory coupled bursting neurons are common in a variety of neural systems from central pattern generators to human brain circuits. One example of the latter is the subcortical…
In networks of periodically firing spiking neurons that are interconnected with chemical synapses, we analyze cluster state, where an ensemble of neurons are subdivided into a few clusters, in each of which neurons exhibit perfect…
This paper is concerned with the study of scalability in nonlinear heterogeneous networks affected by communication delays and disturbances. After formalizing the notion of scalability, we give two sufficient conditions to assess this…
Recently spike timing dependent plasticity was observed in inhibitory synapse in the layer II of entorhinal cortex. The rule provides an interesting zero in the region of $\Delta t=t_{post}-t_{pre}=0$ and in addition the dynamic range of…
The theory of communication through coherence (CTC) proposes that brain oscillations reflect changes in the excitability of neurons, and therefore the successful communication between two oscillating neural populations depends not only on…
Within the RSJ model, we performed a theoretical analysis of phase-locking in elementary strongly coupled Josephson junction cells. For this purpose, we developed a systematic method allowing the investigation of phase-locking in cells with…
The stability of synchronised networked systems is a multi-faceted challenge for many natural and technological fields, from cardiac and neuronal tissue pacemakers to power grids. In the latter case, the ongoing transition to distributed…
For spiking neural networks we consider the stability problem of global synchrony, arguably the simplest non-trivial collective dynamics in such networks. We find that even this simplest dynamical problem -- local stability of synchrony --…
We investigate the stability of synchronization in networks of delay-coupled excitable neural oscillators. On the basis of the master stability function formalism, we demonstrate that synchronization is always stable for excitatory coupling…
Networks of model neurons with balanced recurrent excitation and inhibition produce irregular and asynchronous spiking activity. We extend the analysis of balanced networks to include the known dependence of connection probability on the…
In the study of randomly connected neural network dynamics there is a phase transition from a `simple' state with few equilibria to a `complex' state characterised by the number of equilibria growing exponentially with the neuron…
The dynamics of a multiplex heterogeneous network of oscillators is studied. Two types of similar models based on the Hodgkin-Huxley formalism are used as the basic elements of the networks. The first type model demonstrates bursting…
Many oscillator networks are multistable, meaning that different synchronization states are realized depending on the initial conditions. In this paper, we numerically analyze a ring network of phase oscillators, in which synchronous states…
Large sparse circuits of spiking neurons exhibit a balanced state of highly irregular activity under a wide range of conditions. It occurs likewise in sparsely connected random networks that receive excitatory external inputs and recurrent…
We investigate heterogeneous coupling delays in complex networks of excitable elements described by the FitzHugh-Nagumo model. The effects of discrete as well as of uni- and bimodal continuous distributions are studied with a focus on…
Adaptive Kuramoto models admit a variety of nontrivial phase-locked configurations, including antipodal and rotating-wave states. A central open question is whether the observed persistence of such configurations can be attributed to…
Hopf bifurcation in networks of coupled ODEs creates periodic states in which the relative phases of nodes are well defined near bifurcation. When the network is a fully inhomogeneous nearest-neighbour coupled unidirectional ring, and node…