Period-adding bifurcations and chaos in a periodically stimulated excitable neural relaxation oscillator

This is a pre-print. The definitive version: COOMBES, S. and OSBALDESTIN, A.H., 2000. Period-adding bifurcations and chaos in a periodically stimulated excitable neural relaxation oscillator. Physical Review E, 62(3), pp.4057-4066 Part B.The response of an excitable neuron to trains of electrical spikes is relevant to the understanding of the neural code. In this paper we study a neurobiologically motivated relaxation oscillator, with appropriately identified fast and slow coordinates, that admits an explicit mathematical analysis. An application of geometric singular perturbation theory shows the existence of an attracting invariant manifold which is used to construct the Fenichel normal form for the system. This facilitates the calculation of the response of the system to pulsatile stimulation and allows the construction of a so-called extended isochronal map. The isochronal map is shown to have a single discontinuity and be of a type that can admit three types of response: mode-locked, quasi-periodic and chaotic. The bifurcation structure of the system is seen to be extremely rich and supports period-adding bifurcations separated by windows of both chaos and periodicity. A bifurcation analysis of the isochronal map is presented in conjunction with a description of the various routes to chaos in this system

Modeling Brain Resonance Phenomena Using a Neural Mass Model

Stimulation with rhythmic light flicker (photic driving) plays an important role in the diagnosis of schizophrenia, mood disorder, migraine, and epilepsy. In particular, the adjustment of spontaneous brain rhythms to the stimulus frequency (entrainment) is used to assess the functional flexibility of the brain. We aim to gain deeper understanding of the mechanisms underlying this technique and to predict the effects of stimulus frequency and intensity. For this purpose, a modified Jansen and Rit neural mass model (NMM) of a cortical circuit is used. This mean field model has been designed to strike a balance between mathematical simplicity and biological plausibility. We reproduced the entrainment phenomenon observed in EEG during a photic driving experiment. More generally, we demonstrate that such a single area model can already yield very complex dynamics, including chaos, for biologically plausible parameter ranges. We chart the entire parameter space by means of characteristic Lyapunov spectra and Kaplan-Yorke dimension as well as time series and power spectra. Rhythmic and chaotic brain states were found virtually next to each other, such that small parameter changes can give rise to switching from one to another. Strikingly, this characteristic pattern of unpredictability generated by the model was matched to the experimental data with reasonable accuracy. These findings confirm that the NMM is a useful model of brain dynamics during photic driving. In this context, it can be used to study the mechanisms of, for example, perception and epileptic seizure generation. In particular, it enabled us to make predictions regarding the stimulus amplitude in further experiments for improving the entrainment effect

Small bowtie systems: an enumeration

There exist 3 near bowtie systems of order 7, 12 bowtie systems of order 9, and 1,411,422 balanced bowtie systems of order 13

Narrative Politics in Policy Discourse: The Debate Over Safe Injection Sites in Philadelphia, Pennsylvania

Safe injection sites are spaces where people who inject drugs can do so under the supervision of staff at the sites who attempt to revive them if they overdose. Public officials in Philadelphia, Pennsylvania, have proposed the sites as a means to reduce opioid overdose deaths in the city, a policy proposal that has been politically and legally contested. This article uses the Narrative Politics model to elucidate the concerns, values, and aspirations of the competing narratives in the public discourse over safe injection sites in Philadelphia. Despite the aspirations expressed within the Harm Reduction narrative to open such a site, opposition from the Nimby (not in my backyard) narrative has, at the time of this research, successfully precluded such a step. Other narratives in the discourse include the Abstinence narrative opposing safe injection sites and the Social Justice narrative opposed to incarceration but also hesitant to wholeheartedly endorse the Harm Reduction narrative for its delayed advocacy of compassionate treatment of people who use drugs now that the face of the person who uses opioids is a white one. In addition to juxtaposing competing narratives against one another and considering their alignments, disagreements, and interactions, the authors consider absences and shared presuppositions. The social construction of the purported drug addict varies in some ways between and among the prevailing narratives; in other ways, all the narratives problematize “addiction” as an affliction that justifies techniques of discipline aimed at caring for and controlling the population. </jats:p

Leak rate analysis of the Westinghouse Reactor Coolant Pump

An independent analysis was performed by ETEC to determine what the seal leakage rates would be for the Westinghouse Reactor Coolant Pump (RCP) during a postulated station blackout resulting from loss of ac electric power. The object of the study was to determine leakage rates for the following conditions: Case 1: All three seals function. Case 2: No. 1 seal fails open while Nos. 2 and 3 seals function. Case 3: All three seals fail open. The ETEC analysis confirmed Westinghouse calculations on RCP seal performance for the conditions investigated. The leak rates predicted by ETEC were slightly lower than those predicted by Westinghouse for each of the three cases as summarized below. Case 1: ETEC predicted 19.6 gpm, Westinghouse predicted 21.1 gpm. Case 2: ETEC predicted 64.7 gpm, Westinghouse predicted 75.6 gpm. Case 3: ETEC predicted 422 gpm, Westinghouse predicted 480 gpm. 3 refs., 22 figs., 6 tabs