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, which generate irregular spiking. The chaotic spiking gives rise to irregular bursting. The duration of bursts near the transition can be very long. We describe...

Differential effects of metabotropic glutamate receptor antagonists on bursting activity in the amygdala. Metabotropic glutamate receptors (mGluRs) are implicated in both the activation and inhibition of epileptiform bursting activity in seizure models. We examined the role of mGluR agonists and antagonists on bursting in vitro with whole cell recordings from neurons in the basolateral amygdala...

We describe a classification scheme for bursting oscillations which encompasses many of those found in the literature on bursting in excitable media. This is an extension of the scheme of Rinzel (in Mathematical Topics in Population Biology, Springer, Berlin, 1987), put in the context of a sequence of horizontal cuts through a two-parameter bifurcation diagram. We use this to describe the pheno...

We show that inhibitory networks composed of two endogenously bursting neurons can robustly display several coexistent phase-locked states in addition to stable antiphase and in-phase bursting. This work complements and enhances our recent result [Jalil, Belykh, and Shilnikov, Phys. Rev. E 81, 045201(R) (2010)] that fast reciprocal inhibition can synchronize bursting neurons due to spike intera...

The synchronization of bursting Hindmarsh-Rose neurons coupled by a time-delayed fast threshold modulation synapse was studied. It is shown that there is a domain of the coupling parameter and nonzero time-lag values such that the bursting neurons are exactly synchronized. Furthermore, and contrary to the case of electrical synapses, such synchronous bursting is stochastically stable.

Transcription is episodic, consisting of a series of discontinuous bursts. Using live-imaging methods and quantitative analysis, we examine transcriptional bursting in living Drosophila embryos. Different developmental enhancers positioned downstream of synthetic reporter genes produce transcriptional bursts with similar amplitudes and duration but generate very different bursting frequencies, ...

We present two hypotheses on the mathematical mechanism underlying bursting dynamics in a class of differential systems: (1) that the transition from continuous firing of spikes to bursting is caused by a crisis which destabilizes a chaotic state of continuous spiking; and (2) that the bursting corresponds to a homoclinicity to this unstable chaotic state. These propositions are supported by a ...

The time-delay effect on the bursting of the synchronized state of coupled Hindmarsh-Rose neurons is investigated in this paper. The time-delay influence on the structure of the slow manifold is first studied by using the method of stability switch. And then on the basis of the geometric singular perturbation theory, case studies are given to show that the time delay can suppress the bursting o...

At ANKA, the Karlsruhe synchrotron radiation source, the so called short bunch-length operation mode allows the reduction of the bunch length down to a few picoseconds. The micro-bunching instability resulting from the high degree of longitudinal compression leads to fluctuations in the emitted intensity in the THz regime, referred to as bursting. For extremely compressed bunches at ANKA bursti...

A continuous train of irregularly spaced spikes, peculiar of homoclinic chaos, transforms into clusters of regularly spaced spikes, with quiescent periods in between (bursting regime), by feeding back a low frequency portion of the dynamical output. Such autonomous bursting results to be extremely robust against noise; we provide experimental evidence of it in a CO 2 laser with feedback. The ph...