Cell-to-cell variability plays a critical role in cellular responses and decision-making in a population, and transcriptional bursting has been broadly studied by experimental and theoretical approaches as the potential source of cell-to-cell variability. Although molecular mechanisms of transcriptional bursting have been proposed, there is little consensus. An unsolved key question is whether ...

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...

A two-dimensional map exhibiting chaotic bursting behavior similar to the bursting electrical activity observed in biological neurons and endocrine cells is examined. Model parameters are changed so that the bursting behavior is destroyed. We show that bursting can be recovered in a population of such nonbursting cells when they are coupled via the mean field. The phenomenon is explained with a...

Bursting electrical activity is ubiquitous in excitable cells such as neurons and many endocrine cells. The technique of fast/slow analysis, which takes advantage of time scale differences, is typically used to analyze the dynamics of bursting in mathematical models. Two classes of bursting oscillations that have been identified with this technique, plateau and pseudo-plateau bursting, are ofte...

We study a pair of endogenously bursting neurons with fast nondelayed inhibitory connections. We show that fast reciprocal inhibition, known to facilitate antiphase bursting, can stably synchronize bursting neurons. This contrasts with the classical view that reciprocal inhibition has to be slow or time delayed to establish in-phase synchronization. Through stability analysis, we reveal the eme...

Most types of electrographic epileptiform activity can be characterized by isolated or repetitive bursts in brain electrical activity. This observation is our motivation to determine mechanisms that underlie bursting behavior of neuronal networks. Here we show that the persistent sodium (Na(P)) current in mouse neocortical slices is associated with cellular bursting and our data suggest that th...

Most types of electrographic epileptiform activity can be characterized by isolated or repetitive bursts in brain electrical activity. This observation is our motivation to determine mechanisms that underlie bursting behavior of neuronal networks. Here we show that the persistent sodium current (Na P) in mouse neocortical slices is associated with cellular bursting, and our data suggests that t...

Periodic bursting in fast-slow systems can be viewed as closed paths through the unfolding parameters of degenerate singularities. Using this approach we show that bursting in coupled systems can have interesting behavior. We focus on two identical cell systems and use the Z2 symmetry present in such systems to illustrate interesting bursting phenomena. In particular, we show that Hopf/Hopf mod...

Rhythmically bursting neurons are fundamental to neuronal network function but typically are not considered in the context of primary sensory signaling. We now report intrinsically bursting lobster primary olfactory receptor neurons that respond to odors with a phase-dependent burst of action potentials. Rhythmic odor input as might be generated by sniffing entrains the intrinsic bursting rhyth...