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Developing networks of neural systems can exhibit spontaneous, synchronous activities called neural bursts, which can be important in the organization of functional neural circuits. Before the network matures, the activity level of a burst…
The branching process is the minimal model for propagation dynamics, avalanches and criticality, broadly used in neuroscience. A simple extension of it, adding inhibitory nodes, induces a much-richer phenomenology, including, an…
We examine the stability and qualitative dynamics of stochastic neuronal networks specified as multivariate nonlinear Hawkes processes and related point-process generalized linear models that incorporate both auto- and cross-history…
We investigate the effect of the trapping potential on the quantum phases of strongly correlated ultracold bosons in one-dimensional periodic and quasiperiodic optical lattices. By means of a decoupling meanfield approach, we characterize…
We study the statistical physics of a surprising phenomenon arising in large networks of excitable elements in response to noise: while at low noise, solutions remain in the vicinity of the resting state and large-noise solutions show…
We show the existence of internal stochastic resonance in a microscopic stochastic model for the oscillating CO oxidation on single crystal surfaces. This stochastic resonance arises directly from the elementary reaction steps of the system…
The phenomenon of high-order ($p/q$) synchronization, induced by \textit{two different} frequencies in the system, is well-known and studied extensively in forced oscillators including neurons and to a lesser extent in coupled oscillators.…
Inspired by recent studies on deterministic oscillator models, we introduce a stochastic one-dimensional model for a chain of interacting particles. The model consists of $N$ oscillators performing continuous-time random walks on the…
The presence of both critical behavior and oscillating patterns in brain dynamics is a very interesting issue. In this paper, we consider a model for a neuron population, where each neuron is modeled by an over-damped rotator. We find that…
Chaotic oscillators have gained significant attention in the research community because of their ability to reproduce and investigate the complex dynamics of real-world phenomena. Recent advances in the design of chaotic oscillator…
We report the phenomenon of frequency clustering in a network of Hodgkin-Huxley neurons with spike timing-dependent plasticity. The clustering leads to a splitting of a neural population into a few groups synchronized at different…
In the past decade, synchronization on complex networks has attracted increasing attentions from various research disciplines. Most previous works, however, focus only on the dynamic behaviors of synchronization process in the stable…
The effect of quasi-particle (QP) 'scattering' by the vortex lattice on the de-Haas van-Alphen oscillations in a pure type-II superconductor is investigated within mean field,asymptotic perturbation theory. Using a 2D electron gas model it…
We consider a heterogeneous, globally coupled population of excitatory quadratic integrate-and-fire neurons with excitability adaptation due to a metabolic feedback associated with ketogenic diet, a form of therapy for epilepsy. Bifurcation…
The problem of the effect of two-frequency quasi-periodic perturbations on systems close to arbitrary nonlinear two-dimensional Hamiltonian ones is studied in the case when the corresponding perturbed autonomous systems have a double limit…
We report experimental evidence of the route to spatiotemporal chaos in a large 1D-array of hotspots in a thermoconvective system. Increasing the driving force, a stationary cellular pattern becomes unstable towards a mixed pattern of…
Large nonlinear recurrent neural networks with random couplings generate high-dimensional, potentially chaotic activity whose structure is of interest in neuroscience and other fields. A fundamental object encoding the collective structure…
We show that superconductivity can arise in semiconductors with a band in the shape of a Mexican hat when the chemical potential is tuned close to the band edge, but not intersecting the band, as long as interactions are sufficiently…
We present exact results, as well as some illustrative Monte Carlo simulations, concerning a stochastic network with weighted connections in which the fraction of nodes that are dynamically synchronized is a parameter. This allows one to…
A semiclassical model is used to investigate oscillations of atomic fermions in a combined magnetic trap and one dimensional optical lattice potential following axial displacement of the trap. The oscillations are shown to have a…