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Showing 1 to 16 of 16 for “"Fitzhugh Nagumo"”.
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Non-Classical Symmetry Solutions to the Fitzhugh Nagumo Equation.
… model the behavior of biological phenomena. The Fitzhugh Nagumo partial differential equation is a reaction diffusion equation that arises both in population genetics and in modeling the transmission of action potentials in the nervous system. In this paper we are interested in finding solutions …
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The FitzHugh-Nagumo model dynamics with an application to the hypothalamic pituitary adrenal axis
… 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 …
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Qualitative Models of Neural Activity and the Carleman Embedding Technique.
<p>The two variable Fitzhugh Nagumo model behaves qualitatively like the four variable Hodgkin-Huxley space clamped system and is more mathematically tractable than the Hodgkin Huxley model, thus allowing the action potential and other properties of the Hodgkin Huxley system to be more readily be …
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Nonlinear observer design and synchronization analysis for classical models of neural oscillators
… oscillators, the Hodgkin- Huxley model, the Fitzhugh-Nagumo model, the Morris-Lecar model, and the Hindmarsh-Rose model. Analysis techniques for nonlinear systems were used to develop a set of observers and perform synchronization analysis on the aforementioned neural systems. By using matrix …
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Noise-induced phenomena of signal transmission in excitable neural models
… Neuronenmodellen, insbesondere solche mit FitzHugh-Nagumo Dynamik. Ich beschreibe das Auftreten von vibronischer Resonanz in anregbaren Systemen. Sowohl in einer anregbaren elektronischen Schaltung als auch im FitzHugh-Nagumo Modell zeige ich, daß eine optimale Amplitude einer …
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The Geometry of Isochrons in Planar Systems
… the isochrons of a periodic orbit in the FitzHugh-Nagumo system, an example from the 1970s of a system with two time scales for which the overall structure of the isochrons could not be determined with the computational methods of that time. We show, via numerical continuation, that the …
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Dynamical mechanisms of neural firing irregularity and modulation sensitivity with applications to cochlear implants
… mechanism. Specifically, we show in the Fitzhugh-Nagumo (FN) model that the stability to perturbations such as noise depends upon the stimulation rate. At sufficiently high rates a dynamical instability arises that accounts for the main statistical features of the irregular discharge …
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Incremental proper orthogonal decomposition for PDE simulation data: Algorithms and analysis
… computations for a 1D Burgers' equation, a 1D FitzHugh-Nagumo PDE system, and a 2D Navier-Stokes problem"--Abstract, page iv.</p>
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Steady-State Poisson-Nernst-Planck Systems: Asymptotic expansions and applications to ion channels
… cubic-like assumption of the I-V relation in the FitzHugh-Nagumo model for action potential involving a population of ion channels. However, applications of the results of this thesis to ion channels are limited, since we considered a simplified model with two species of ions and a zero permanent …
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Hardware implementation for cardiac electrical excitation and conduction using an FPGA
… analysis system has been developed based on FitzHugh-Nagumo (FHN) model for a mammalian cardiac ventricular cell. In this research, one dimensional (1D) ring-shaped cable model with 80 compartments of the cell model designed using MATLAB Simulink blocks is able to be converted into …
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Input/output analysis: graphical and algorithmic methods
… the classical van der Pol oscillator and the FitzHugh-Nagumo model of an excitable neuron, which both consist of an LTI transfer function in parallel with monotone and anti-monotone nonlinear resistors. A new algorithm, the difference-of-monotone Douglas-Rachford algorithm, is proposed, which …
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Pattern formation in oscillatory systems
… topics in this dissertation: Kuramoto model and FitzHugh-Nagumo (FHN) model. Kuramoto's original analysis of his model gives the critical synchronization value for K (K is the coupling constant ). He also gives an estimate for the value of order parameter r when K is close to critical point Kc. …
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Numerical approximation of Stratonovich SDEs and SPDEs
… the speed of the waves for the stochastic Nagumo and FitzHugh-Nagumo models. The wave position and hence the speed is found by minimising the L2 distance between a reference function and the travelling wave. While the results obtained from the two different approaches agree, we observe that …
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Identification of Dendritic Processing in Spiking Neural Circuits
… models such as Hodgkin-Huxley, Morris-Lecar, Fitzhugh-Nagumo, as well as simpler models of the integrate-and-fire and threshold-and-fire type. The aggregate time-varying current driving the spike generator is taken to be produced by a dendritic stimulus processor, which is a nonlinear …
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Predicting and identifying signs of criticality near neuronal phase transition
… compare three different implementations of the FitzHugh--Nagumo single spiking neuron model: a mathematical model by H. R. Wilson, an alternative due to Keener and Sneyd, and an op-amp based nonlinear oscillator circuit. Although all three models can produce nonlinear ``spiking" oscillations, …
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Modeling And Detection Of Uterine Contractions Using Magnetomyography
… Here we introduce a modified version of the Fitzhugh-Nagumo: FHN) equation for modeling ionic currents in each myocyte, assuming a plateau-type transmembrane potential. We incorporate the anisotropic nature of the uterus by considering conductivity tensors in our model. In particular, we …