Related papers: Transition to chaos in random networks with cell-t…

Shedding light onto how biological systems represent, process and store information in noisy environments is a key and challenging goal. A stimulating, though controversial, hypothesis poses that operating in dynamical regimes near the edge…

Neural networks with recurrent asymmetric couplings are important to understand how episodic memories are encoded in the brain. Here, we integrate the experimental observation of wide synaptic integration window into our model of sequence…

Coherent oscillatory activity can arise spontaneously as a result of increased coupling in a system of excitable and passive cells, each being quiescent in isolation. This can potentially explain the appearance of spontaneous rhythmic…

We consider two neuronal networks coupled by long-range excitatory interactions. Oscillations in the gamma frequency band are generated within each network by local inhibition. When long-range excitation is weak, these oscillations…

Functional networks provide a topological description of activity patterns in the brain, as they stem from the propagation of neural activity on the underlying anatomical or structural network of synaptic connections. This latter is well…

The brain's functional connectivity fluctuates over time instead of remaining steady in a stationary mode even during the resting state. This fluctuation establishes the dynamical functional connectivity that transitions in a non-random…

The mathematical theory of pattern formation in electrically coupled networks of excitable neurons forced by small noise is presented in this work. Using the Freidlin-Wentzell large deviation theory for randomly perturbed dynamical systems…

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…

A network with local dynamics of logistic type is considered. We implement a mean-field multiplicative coupling among first-neighbor nodes. When the coupling parameter is small the dynamics is dissipated and there is no activity: the…

The ability of discrete-time nonlinear recurrent neural networks to store time-varying small input signals is investigated by mean-field theory. The combination of a small input strength and mean-field assumptions makes it possible to…

We consider continuous time Hopfield-like recurrent networks as dynamical models for gene regulation and neural networks. We are interested in networks that contain n high-degree nodes preferably connected to a large number of Ns weakly…

It is widely accepted that the complex dynamics characteristic of recurrent neural circuits contributes in a fundamental manner to brain function. Progress has been slow in understanding and exploiting the computational power of recurrent…

We study deterministic continuous-time lossy dynamical flow networks with constant exogenous demands, fixed routing, and finite flow and buffer capacities. In the considered model, when the total net flow in a cell ---consisting of the…

Here we numerically study a model of excitable media, namely, a network with occasionally quiet nodes and connection weights that vary with activity on a short-time scale. Even in the absence of stimuli, this exhibits unstable dynamics,…

We propose a discrete time dynamical system (a map) as phenomenological model of excitable and spiking-bursting neurons. The model is a discontinuous two-dimensional map. We find condition under which this map has an invariant region on the…

We study emergent oscillatory behavior in networks of diffusively coupled nonlinear ordinary differential equations. Starting from a situation where each isolated node possesses a globally attracting equilibrium point, we give, for an…

We study statistical properties of the irregular bursting arising in a class of neuronal models close to the transition from spiking to bursting. Prior to the transition to bursting, the systems in this class develop chaotic attractors,…

The mammalian brain could contain dense and sparse network connectivity structures, including both excitatory and inhibitory neurons, but is without any clearly defined output layer. The neurons have time constants, which mean that the…

High-dimensional chaotic dynamics can emerge in a large random recurrent neural network when the synaptic gain crosses a threshold. Recent works showed that the kinetic energy of neural activity links the chaotic dynamics and the supporting…

The use of artificial neural networks as models of chaotic dynamics has been rapidly expanding. Still, a theoretical understanding of how neural networks learn chaos is lacking. Here, we employ a geometric perspective to show that neural…