Related papers: A novel canard-based mechanism for mixed-mode osci…
In this paper, we develop and analyze a model that studies the interaction between a specialist predator, a generalist predator, and their common prey in a two-trophic ecosystem featuring three timescales. We assume that the prey operates…
A universal mechanism of emergence of synchronized low frequency brain wave field activity is presented as a result of nonlinear coupling with flat frequency neuronal forcing. The mechanism utilizes a unique dispersion properties of…
The multiple time scale dynamics induced by radiation pressure and photothermal effects in a high-finesse optomechanical resonator is experimentally studied. At difference with two-dimensional slow-fast systems, the transition from the…
Oscillations of free intracellular calcium concentration are thought to be important in the control of a wide variety of physiological phenomena, and there is long-standing interest in understanding these oscillations via the investigation…
In the cerebral cortex, neurons are subject to a continuous bombardment of synaptic inputs originating from the network's background activity. This leads to ongoing, mostly subthreshold membrane dynamics that depends on the statistics of…
We present a first-order non-homogeneous Markov model for the interspike-interval density of a continuously stimulated spiking neuron. The model allows the conditional interspike-interval density and the stationary interspike-interval…
Neurons in the nervous system are submitted to distinct sources of noise, such as ionic-channel and synaptic noise, which introduces variability in their responses to repeated presentations of identical stimuli. This motivates the use of…
Recurrent networks of dynamic elements frequently exhibit emergent collective oscillations, which can display substantial regularity even when the individual elements are considerably noisy. How noise-induced dynamics at the local level…
Recurrently coupled networks of inhibitory neurons robustly generate oscillations in the gamma band. Nonetheless, the corresponding Wilson-Cowan type firing rate equation for such an inhibitory population does not generate such oscillations…
Single trial analyses of ensemble activity in alert animals demonstrate that cortical circuits dynamics evolve through temporal sequences of metastable states. Metastability has been studied for its potential role in sensory coding, memory…
Generation of mechanical oscillation is ubiquitous to wide variety of intracellular processes. We show that catchbonding behaviour of motor proteins provides a generic mechanism of generating spontaneous oscillations in motor-cytoskeletal…
Networks of stochastic spiking neurons are interesting models in the area of Theoretical Neuroscience, presenting both continuous and discontinuous phase transitions. Here we study fully connected networks analytically, numerically and by…
Cortical neural circuits display highly irregular spiking in individual neurons but variably sized collective firing, oscillations and critical avalanches at the population level, all of which have functional importance for information…
A classical view of neural coding relies on temporal firing synchrony among functional groups of neurons; however the underlying mechanism remains an enigma. Here we experimentally demonstrate a mechanism where time-lags among neuronal…
In the classic view of cortical rhythms, the interaction between excitatory pyramidal neurons (E) and inhibitory parvalbumin neurons (I) has been shown to be sufficient to generate gamma and beta band rhythms. However, it is now clear that…
Understanding of short-term synaptic depression (STSD) and other forms of synaptic plasticity is a topical problem in neuroscience. Here we study the role of STSD in the formation of complex patterns of brain rhythms. We use a cortical…
A complex interplay of single-neuron properties and the recurrent network structure shapes the activity of cortical neurons. The single-neuron activity statistics differ in general from the respective population statistics, including…
In this article, we study a system of reaction-diffusion equations in which the diffusivities are widely separated. We report on the discovery of families of spatially periodic canard solutions that emerge from {\em singular Turing…
Cortical neurons are bistable; as a consequence their local field potentials can fluctuate between quiescent and active states, generating slow 0.5-2 Hz oscillations which are widely known as transitions between Up and Down States. Despite…
We describe the fast-slow dynamics of two FitzHugh--Nagumo equations coupled symmetrically through the slow equations. We use symmetry arguments to find a non-empty open set of parameter values for which the two equations synchronise, and…