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We study the use of the FitzHugh-Nagumo (FHN) model for capturing neural spiking. The FHN model is a widely used approximation of the Hodgkin-Huxley model that has significant limitations. In particular, it cannot produce the key spiking behavior of bursting. We illustrate that by allowing time-varying parameters for the FHN model, these limitations can be(More)
The pulsatile release of cortisol from the adrenal glands is controlled by a hierarchical system that involves corticotropin releasing hormone (CRH) from the hypothalamus, adrenocorticotropin hormone (ACTH) from the pituitary, and cortisol from the adrenal glands. Determining the number, timing, and amplitude of the cortisol secretory events and recovering(More)
In this thesis, I revisit the issue of the utility of the FitzHugh-Nagumo (FHN) model for capturing neuron firing behaviors. It has been noted (e.g., see [8]) that the FHN model cannot exhibit certain interesting firing behaviors such as bursting. I will illustrate that, by allowing time-varying parameters for the FHN model, one could overcome such(More)
Large systems of coupled oscillators subjected to a periodic external drive occur in many situations in physics and biology. Here the simple paradigmatic case of equal strength, all-to-all sine coupling of phase oscillators subject to a sinusoidal external drive, is considered. The stationary states and their stability are determined. Using the stability(More)
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Abstract— In this paper, we revisit the issue of the utility of the(More)
Existing mathematical models for cortisol secretion do not describe the entire cortisol secretion process, from the neural firing of corticotropin releasing hormone (CRH) in the hypothalamus to cortisol concentration in the plasma. In this paper, we lay the groundwork to construct a more comprehensive model, relating CRH, Adrenocorticotropic hormone (ACTH),(More)
In this paper, we revisit the issue of the utility of the FitzHugh-Nagumo (FHN) model for capturing neuron firing behaviors. It has been noted (e.g., see [6]) that the FHN model cannot exhibit certain interesting firing behaviors such as bursting. We illustrate that, by allowing time-varying parameters for the FHN model, one could overcome such limitations(More)
An important question in neuroscience is understanding the relationship between high-dimensional electrophysiological data and complex, dynamic behavioral data. One general strategy to address this problem is to define a low-dimensional representation of essential cognitive features describing this relationship. Here we describe a general state-space method(More)
Electrodermal activity (EDA) is a measure of physical arousal, which is frequently measured during psychophysical tasks relevant for anxiety disorders. Recently, specific protocols and procedures have been devised in order to examine the neural mechanisms of fear conditioning and extinction. EDA reflects important responses associated with stimuli(More)