Electrical activities are ubiquitous neuronal bioelectric phenomena, which have many different modes to encode the expression of biological information, and constitute the whole process of signal propagation between neurons. Therefore, we focus on the electrical activities of neurons, which is also causing widespread concern among neuroscientists. In this paper, we mainly investigate the electr...

Fluid parcels can exchange water properties when coming into contact with each other, leading to mixing. The trajectory encounter mass and a related simplified quantity, the encounter volume, are introduced as a measure of the mixing potential of a flow. The encounter volume quantifies the volume of fluid that passes close to a reference trajectory over a finite time interval. Regions character...

We study an influence of white Gaussian noise on synchrony of neural oscillators. In neurophysiology, the property of a single neuron to provide identical outputs for repeated noisy input (in terms of our problem, an array of such identical neurons driven by common noise to behave synchronously) is referred as “reliability” [1]. The first quantifier of the synchrony we use is the Lyapunov expon...

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Chapter 1 Preliminary concepts and literature review . . . . . . . . . . . . . . . 11 1.1 Cellular excitability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.1.1 Membranes, ionic gradients, and transport . . . . . . . . . . . . . 12 1.1.2 Electrical signaling and action potentials . . . . . . . . . . ...

When each site of a spatially extended excitable medium is independently driven by a Poisson stimulus with rate h , the interplay between creation and annihilation of excitable waves leads to an average activity F . It has recently been suggested that in the low-stimulus regime (h approximately 0) the response function F(h) of hypercubic deterministic systems behaves as a power law, F approxima...

Stochastic event synchrony (SES) is a recently proposed family of similarity measures. First, "events" are extracted from the given signals; next, one tries to align events across the different time series. The better the alignment, the more similar the N time series are considered to be. The similarity measures quantify the reliability of the events (the fraction of "nonaligned" events) and th...

We examine the behavior in the presence of noise of an array of Morris-Lecar neurons coupled via chemical synapses. Special attention is devoted to comparing this behavior with the better known case of electrical coupling arising via gap junctions. In particular, our numerical simulations show that chemical synapses are more efficient than gap junctions in enhancing coherence at an optimal nois...

Seizure control using deep brain stimulation (DBS) provides an alternative therapy to patients with intractable and drug resistant epilepsy. This paper presents novel DBS stimulus protocols to disrupt seizures. Two protocols are presented: open-loop stimulation and a closed-loop feedback system utilizing measured firing rates to adjust stimulus frequency. Stimulation suppression is demonstrated...

We propose a biophysical mechanism for the high interspike interval variability observed in cortical spike trains. The key lies in the nonlinear dynamics of cortical spike generation, which are consistent with type I membranes where saddle-node dynamics underlie excitability (Rinzel & Ermentrout, 1989). We present a canonical model for type I membranes, the theta-neuron. The theta-neuron is a p...

The cardiac ganglion (CG) of Homarus americanus is a central pattern generator that consists of two oscillatory groups of neurons: "small cells" (SCs) and "large cells" (LCs). We have shown that SCs and LCs begin their bursts nearly simultaneously but end their bursts at variable phases. This variability contrasts with many other central pattern generator systems in which phase is well maintain...