Displaying similar documents to “The mathematics of Kuramoto models which describe synchronization phenomena”

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.

Branching processes and models of epidemics

R. Bartoszyński

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CONTEXTS0. Introduction.......................................................................................................................................................................... 5Part IMODELS OF EPIDEMICS FOli INFECTIOUS DISEASES1. Informal description of the phenomenon of epidemics and constructionof mathematical models...........................................................................................................................................................

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 Modeling Framework For Immune-related Diseases

F. Castiglione, S. Motta, F. Pappalardo, M. Pennisi (2012)

Mathematical Modelling of Natural Phenomena

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About twenty five years ago the first discrete mathematical model of the immune system was proposed. It was very simple and stylized. Later, many other computational models have been proposed each one adding a certain level of sophistication and detail to the description of the system. One of these, the Celada-Seiden model published back in 1992, was already mature at its birth, setting apart from the topic-specific nature of the other ...

Using normal mode analysis in teaching mathematical modeling to biology students

D. A. Kondrashov (2011)

Mathematical Modelling of Natural Phenomena

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Linear oscillators are used for modeling a diverse array of natural systems, for instance acoustics, materials science, and chemical spectroscopy. In this paper I describe simple models of structural interactions in biological molecules, known as elastic network models, as a useful topic for undergraduate biology instruction in mathematical modeling. These models use coupled linear oscillators to model the fluctuations of molecular structures around the equilibrium state. I present many...

Fragmentation-Coagulation Models of Phytoplankton

Ryszard Rudnicki, Radosław Wieczorek (2006)

Bulletin of the Polish Academy of Sciences. Mathematics

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We present two new models of the dynamics of phytoplankton aggregates. The first one is an individual-based model. Passing to infinity with the number of individuals, we obtain an Eulerian model. This model describes the evolution of the density of the spatial-mass distribution of aggregates. We show the existence and uniqueness of solutions of the evolution equation.

The Notion of Model in Software Engineering Понятието модел в софтуерните технологии

Sredkov, Miloslav (2011)

Union of Bulgarian Mathematicians

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Милослав A. Средков - Понятията модел и моделиране се използват толкова интензивно в много дисциплини, че е трудно да им се придаде конретно значение. Дори в Софтуерните технологии, разбирането на тези понятия силно зависи от контекста. Ние смятаме, че това допринася за неконсистентността между подходите за моделиране там. В тази статия посочваме някои от произтичащите проблеми, както и важността да има подходяща дефиниция, съчетана с подходящи инструменти. Преглеждаме по-общите дефиниции...

Multilevel Modeling of the Forest Resource Dynamics

I. N. Vladimirov, A. K. Chudnenko (2009)

Mathematical Modelling of Natural Phenomena

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We examine the theoretical and applications-specific issues relating to modeling the temporal and spatial dynamics of forest ecosystems, based on the principles of investigating dynamical models. When developing the predictive dynamical models of forest resources, there is a possibility of achieving uniqueness of the solutions to equations by taking into account the initial and boundary conditions of the solution, and the conditions of the geographical environment. We present the results...

A Coherent Derivation of an Average Ion Model Including the Evolution of Correlations Between Different Shells

Daniel Bouche, Alain Decoster, Laurent Desvillettes, Valeria Ricci (2013)

MathematicS In Action

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We propose in this short note a method enabling to write in a systematic way a set of refined equations for average ion models in which correlations between populations are taken into account, starting from a microscopic model for the evolution of the electronic configuration probabilities. Numerical simulations illustrating the improvements with respect to standard average ion models are presented at the end of the paper.