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Search results for: spiking dynamics
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Analysis of dynamics of a map-based neuron model via Lorenz maps
PublicationModeling nerve cells can facilitate formulating hypotheses about their real behavior and improve understanding of their functioning. In this paper, we study a discrete neuron model introduced by Courbage et al. [Chaos 17, 043109 (2007)], where the originally piecewise linear function defining voltage dynamics is replaced by a cubic polynomial, with an additional parameter responsible for varying the slope. Showing that on a large...
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Spike patterns and chaos in a map-based neuron model
PublicationThe work studies the well-known map-based model of neuronal dynamics introduced in 2007 by Courbage, Nekorkin and Vdovin, important due to various medical applications. We also review and extend some of the existing results concerning β-transformations and (expanding) Lorenz mappings. Then we apply them for deducing important properties of spike-trains generated by the CNV model and explain their implications for neuron behaviour....
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Integrate-and-fire models with an almost periodic input function
PublicationWe investigate leaky integrate-and-fire models (LIF models for short) driven by Stepanov and μ-almost periodic functions. Special attention is paid to the properties of the firing map and its displacement, which give information about the spiking behavior of the considered system. We provide conditions under which such maps are well-defined and are uniformly continuous. We show that the LIF models with Stepanov almost periodic...
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Combined Single Neuron Unit Activity and Local Field Potential Oscillations in a Human Visual Recognition Memory Task
PublicationGOAL: Activities of neuronal networks range from action potential firing of individual neurons, coordinated oscillations of local neuronal assemblies, and distributed neural populations. Here, we describe recordings using hybrid electrodes, containing both micro- and clinical macroelectrodes, to simultaneously sample both large-scale network oscillations and single neuron spiking activity in the medial temporal lobe structures...
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Sathwik Prathapagiri
PeopleSathwik was born in 2000. In 2022, he completed his Master’s of Science in Biological Sciences and Bachelor’s of Engineering in Chemical Engineering in an integrated dual degree program from Birla Institute Of Technology And Science, Pilani, India. During his final year, he worked as a research intern under Dr Giri P Krishnan at Bazhenov lab, University of California San Diego school of medicine to pursue his Master’s Thesis on...
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Wild oscillations in a nonlinear neuron model with resets: (I) Bursting, spike-adding and chaos
PublicationIn a series of two papers, we investigate the mechanisms by which complex oscillations are generated in a class of nonlinear dynamical systems with resets modeling the voltage and adaptation of neurons. This first paper presents mathematical analysis showing that the system can support bursts of any period as a function of model parameters, and that these are organized in a period-incrementing structure. In continuous dynamical...