Related papers: Transition from asynchronous to oscillatory dynami…
Neural circuits exhibit complex activity patterns, both spontaneously and evoked by external stimuli. Information encoding and learning in neural circuits depend on how well time-varying stimuli can control spontaneous network activity. We…
Large networks of spiking neurons show abrupt changes in their collective dynamics resembling phase transitions studied in statistical physics. An example of this phenomenon is the transition from irregular, noise-driven dynamics to…
Neuronal networks alternate between high- and low-activity regimes, known as up and down states. They also display rhythmic patterns essential for perception, memory consolidation, and sensory processing. Despite their importance, the…
In many real-world oscillator systems, the phase response curves are highly heterogeneous. However, dynamics of heterogeneous oscillator networks has not been seriously addressed. We propose a theoretical framework to analyze such a system…
At the macroscale, the brain operates as a network of interconnected neuronal populations, which display rhythmic dynamics that support interareal communication. Understanding how stimulation of a particular brain area impacts such…
Theoretical studies of synchronization are usually based on models of coupled phase oscillators which, when isolated, have constant angular frequency. Stochastic discrete versions of these uniform oscillators have also appeared in the…
Complex networks, from neuronal assemblies to social systems, can exhibit abrupt, system-wide transitions without external forcing. These endogenously generated ``noise-induced transitions'' emerge from the intricate interplay between…
We analyze the emergent regimes and the stimulus-response relationship of a population of noisy map neurons by means of a mean-field model, derived within the framework of cumulant approach complemented by the Gaussian closure hypothesis.…
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…
Neural network dynamics emerge from the interaction of spiking cells. One way to formulate the problem is through a theoretical framework inspired by ideas coming from statistical physics, the so-called mean-field theory. In this document,…
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…
Oscillators coupled in a network can synchronize with each other to yield a coherent population rhythm. If multiple such networks are coupled together, the question arises whether these rhythms will synchronize. We investigate the impact of…
Memristors have uses as artificial synapses and perform well in this role in simulations with artificial spiking neurons. Our experiments show that memristor networks natively spike and can exhibit emergent oscillations and bursting spikes.…
Author summary: Synchronization of neuronal spiking in the brain is related to cognitive functions, such as perception, attention, and memory. It is therefore important to determine which properties of neurons influence their collective…
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 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,…
A regime of coexistence of asynchronous and clustered dynamics is analyzed for globally coupled homogeneous and heterogeneous inhibitory networks of quadratic integrate-and-fire (QIF) neurons subject to Gaussian noise. The analysis is based…
The generalization properties of an attractive network of non monotonic neurons which infers concepts from samples are studied. The macroscopic dynamics for the overlap between the state of the neurons with the concepts, well as the…
We propose a model of an adaptive network of spiking neurons that gives rise to a hypernetwork of its dynamic states at the upper level of description. Left to itself, the network exhibits a sequence of transient clustering which relates to…
We report on finite-sized-induced transitions to synchrony in a population of phase oscillators coupled via a nonlinear mean field, which microscopically is equivalent to a hypernetwork organization of interactions. Using a self-consistent…