Related papers: Phase-locking in weakly heterogeneous neuronal net…
Physiological networks are usually made of a large number of biological oscillators evolving on a multitude of different timescales. Phase oscillators are particularly useful in the modelling of the synchronization dynamics of such systems.…
We consider an excitatory random network of leaky integrate-and-fire pulse coupled neurons. The neurons are connected as in a directed Erd\"os-Renyi graph with average connectivity $<k>$ scaling as a power law with the number of neurons in…
We revisit the dynamics of a prototypical model of balanced activity in networks of spiking neutrons. A detailed investigation of the thermodynamic limit for fixed density of connections (massive coupling) shows that, when inhibition…
Biological information processing is often carried out by complex networks of interconnected dynamical units. A basic question about such networks is that of reliability: if the same signal is presented many times with the network in…
For general networks of pulse-coupled oscillators, including regular, random, and more complex networks, we develop an exact stability analysis of synchronous states. As opposed to conventional stability analysis, here stability is…
The dynamics of complex-valued fractional-order neuronal networks are investigated, focusing on stability, instability and Hopf bifurcations. Sufficient conditions for the asymptotic stability and instability of a steady state of the…
In a manner similar to the molecular chaos that underlies the stable thermodynamics of gases, neuronal system may exhibit microscopic instability in individual neuronal dynamics while a macroscopic order of the entire population possibly…
Detailed experimental and theoretical investigations on two coupled fiber lasers, each with many longitudinal modes, reveal that the behavior of the longitudinal modes depends on both the coupling strength as well as the detuning between…
We study fully synchronized (coherent) states in complex networks of chaotic oscillators, reviewing the analytical approach of determining the stability conditions for synchronizability and comparing them with numerical criteria. As an…
We investigate spatio-temporal patterns occurring in a two-layer multiplex network of oscillatory FitzHugh-Nagumo neurons, where each layer is represented by a nonlocally coupled ring. We show that weak multiplexing, i.e., when the coupling…
For infinitely large sparse networks of spiking neurons mean field theory shows that a balanced state of highly irregular activity arises under various conditions. Here we analytically investigate the microscopic irregular dynamics in…
We study dynamics of phase-differences (PDs) of coupled oscillators where both the intrinsic frequencies and the couplings vary in time. In case the coupling coefficients are all nonnegative, we prove that the PDs are asymptotically stable…
We investigate the existence and stability of travelling wave solutions in a continuum field of non-locally coupled identical phase oscillators with distance-dependent propagation delays. A comprehensive stability diagram in the parametric…
Dynamical systems with a coupled cell network structure can display synchronous solutions, spectral degeneracies and anomalous bifurcation behavior. We explain these phenomena here for homogeneous networks, by showing that every homogeneous…
Networks of randomly connected neurons are among the most popular models in theoretical neuroscience. The connectivity between neurons in the cortex is however not fully random, the simplest and most prominent deviation from randomness…
We introduce a simple model of static networks, where nodes are located on a ring structure, and two accompanying dynamic rules of repeated averaging on periodic node states. We assume nodes can interact with neighbors, and will add…
We demonstrate that solitary states can be widely observed for networks of coupled oscillators with local, non-local and global couplings, and they preserve in both thermodynamic and Hamiltonian limits. We show that depending on units' and…
The problem of synchronization in heterogeneous networks of linear systems with nonlinear delayed diffusive coupling is considered. The network is presented in new coordinates mean-field dynamics and synchronization errors. Thus the problem…
Precise timing of spikes and temporal locking are key elements of neural computation. Here we demonstrate how even strongly heterogeneous, deterministic neural networks with delayed interactions and complex topology can exhibit periodic…
A general phase reduction method for a network of coupled dynamical elements exhibiting collective oscillations, which is applicable to arbitrary networks of heterogeneous dynamical elements, is developed. A set of coupled adjoint equations…