Displaying similar documents to “Canonical models in mathematical neuroscience.”

A Suite of Skeleton Models for the MJO with Refined Vertical Structure

Sulian Thual, Andrew J. Majda (2015)

Mathematics of Climate and Weather Forecasting

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The Madden-Julian oscillation (MJO) is the dominant mode of variability in the tropical atmosphere on intraseasonal timescales and planetary spatial scales. The skeleton model is a minimal dynamical model that recovers robustly the most fundamental MJO features of (I) a slow eastward speed of roughly 5 ms−1, (II) a peculiar dispersion relation with dw/dk ≈ 0, and (III) a horizontal quadrupole vortex structure. This model depicts the MJO as a neutrally-stable atmosphericwave that involves...

A model of cardiac tissue as an excitable medium with two interacting pacemakers having refractory time

Alexander Loskutov, Sergei Rybalko, Ekaterina Zhuchkova (2003)

Banach Center Publications

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A quite general model of the nonlinear interaction of two impulse systems describing some types of cardiac arrhythmias is developed. Taking into account a refractory time the phase locking phenomena are investigated. Effects of the tongue splitting and their interweaving in the parametric space are found. The results obtained allow us to predict the behavior of excitable systems with two pacemakers depending on the type and intensity of their interaction and the initial phase. ...

Multidimensional Models for Methodological Validation in Multifractal Analysis

R. Lopes, I. Bhouri, S. Maouche, P. Dubois, M. H. Bedoui, N. Betrouni (2008)

Mathematical Modelling of Natural Phenomena

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Multifractal analysis is known as a useful tool in signal analysis. However, the methods are often used without methodological validation. In this study, we present multidimensional models in order to validate multifractal analysis methods.

Viscosity solutions to a new phase-field model for martensitic phase transformations

Zhu, Peicheng

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We investigate a new phase-field model which describes martensitic phase transitions, driven by material forces, in solid materials, e.g., shape memory alloys. This model is a nonlinear degenerate parabolic equation of second order, its principal part is not in divergence form in multi-dimensional case. We prove the existence of viscosity solutions to an initial-boundary value problem for this model.

Modelling Circadian Rhythms in Drosophila and Investigation of VRI and PDP1 Feedback Loops Using a New Mathematical Model

D. Kulasiri, Z. Xie (2008)

Mathematical Modelling of Natural Phenomena

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We present a brief review of molecular biological basis and mathematical modelling of circadian rhythms in . We discuss pertinent aspects of a new model that incorporates the transcriptional feedback loops revealed so far in the network of the circadian clock (PER/TIM and VRI/PDP1 loops). Conventional Hill functions are not used to describe the regulation of genes, instead the explicit reactions of binding and unbinding processes of transcription factors to promoters are probabilistically...