Journal ArticleESAIM: Mathematical Modelling and Numerical Analysis · January 1, 2010
While alternans in a single cardiac cell appears through a simple period-doubling bifurcation, in extended tissue the exact nature of the bifurcation is unclear. In particular, the phase of alternans can exhibit wave-like spatial dependence, either station ...
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Journal ArticleSIAM Journal on Applied Mathematics · December 1, 2008
Under rapid periodic pacing, cardiac cells typically undergo a period-doubling bifurcation in which action potentials of short and long duration alternate with one another. If these action potentials propagate in a fiber, the short-long alternation may suf ...
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Journal ArticleSIAM Journal on Applied Mathematics · December 1, 2008
This paper studies a parsimonious model of landslide motion, which consists of the one-dimensional diffusion equation (for pore pressure) coupled through a boundary condition to a first-order ODE (Newton's second law). Velocity weakening of sliding frictio ...
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Journal ArticleNonlinear dynamics · January 2008
Cardiac restitution has been described both in terms of ionic models-systems of ODE's-and in terms of mapping models. While the former provide a more fundamental description, the latter are more flexible in trying to fit experimental data. Recently we prop ...
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Journal ArticleNonlinear dynamics · November 2007
Unlike classical bifurcations, border-collision bifurcations occur when, for example, a fixed point of a continuous, piecewise C1 map crosses a boundary in state space. Although classical bifurcations have been much studied, border-collision bifurcations a ...
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Journal ArticlePhysical review letters · August 2007
We investigate, both experimentally and theoretically, the period-doubling bifurcation to alternans in heart tissue. Previously, this phenomenon has been modeled with either smooth or border-collision dynamics. Using a modification of existing experimental ...
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Journal ArticleNonlinear dynamics · June 2007
Various authors have shown that, near the onset of a period-doubling bifurcation, small perturbations in the control parameter may result in much larger disturbances in the response of the dynamical system. Such amplification of small signals can be measur ...
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Journal ArticleBulletin of mathematical biology · February 2007
Many features of the sequence of action potentials produced by repeated stimulation of a patch of cardiac muscle can be modeled by a 1D mapping, but not the full behavior included in the restitution portrait. Specifically, recent experiments have found tha ...
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Journal ArticleSIAM Journal on Applied Mathematics · June 7, 2004
Jenike's radial solution, widely used in the design of materials-handling equipment, is a similarity solution of steady-state continuum equations for the flow under gravity of granular material through an infinite, right-circular cone. In this paper we stu ...
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Journal ArticleESAIM: Mathematical Modelling and Numerical Analysis · January 1, 2010
While alternans in a single cardiac cell appears through a simple period-doubling bifurcation, in extended tissue the exact nature of the bifurcation is unclear. In particular, the phase of alternans can exhibit wave-like spatial dependence, either station ...
Full textOpen AccessCite
Journal ArticleSIAM Journal on Applied Mathematics · December 1, 2008
Under rapid periodic pacing, cardiac cells typically undergo a period-doubling bifurcation in which action potentials of short and long duration alternate with one another. If these action potentials propagate in a fiber, the short-long alternation may suf ...
Full textOpen AccessCite
Journal ArticleSIAM Journal on Applied Mathematics · December 1, 2008
This paper studies a parsimonious model of landslide motion, which consists of the one-dimensional diffusion equation (for pore pressure) coupled through a boundary condition to a first-order ODE (Newton's second law). Velocity weakening of sliding frictio ...
Full textCite
Journal ArticleNonlinear dynamics · January 2008
Cardiac restitution has been described both in terms of ionic models-systems of ODE's-and in terms of mapping models. While the former provide a more fundamental description, the latter are more flexible in trying to fit experimental data. Recently we prop ...
Full textCite
Journal ArticleNonlinear dynamics · November 2007
Unlike classical bifurcations, border-collision bifurcations occur when, for example, a fixed point of a continuous, piecewise C1 map crosses a boundary in state space. Although classical bifurcations have been much studied, border-collision bifurcations a ...
Full textCite
Journal ArticlePhysical review letters · August 2007
We investigate, both experimentally and theoretically, the period-doubling bifurcation to alternans in heart tissue. Previously, this phenomenon has been modeled with either smooth or border-collision dynamics. Using a modification of existing experimental ...
Full textCite
Journal ArticleNonlinear dynamics · June 2007
Various authors have shown that, near the onset of a period-doubling bifurcation, small perturbations in the control parameter may result in much larger disturbances in the response of the dynamical system. Such amplification of small signals can be measur ...
Full textCite
Journal ArticleBulletin of mathematical biology · February 2007
Many features of the sequence of action potentials produced by repeated stimulation of a patch of cardiac muscle can be modeled by a 1D mapping, but not the full behavior included in the restitution portrait. Specifically, recent experiments have found tha ...
Full textCite
Journal ArticleSIAM Journal on Applied Mathematics · June 7, 2004
Jenike's radial solution, widely used in the design of materials-handling equipment, is a similarity solution of steady-state continuum equations for the flow under gravity of granular material through an infinite, right-circular cone. In this paper we stu ...
Full textCite
Journal ArticleBulletin of mathematical biology · September 2003
In this paper we introduce and study a model for electrical activity of cardiac membrane which incorporates only an inward and an outward current. This model is useful for three reasons: (1) Its simplicity, comparable to the FitzHugh-Nagumo model, makes it ...
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Journal ArticlePhysical review. E, Statistical, nonlinear, and soft matter physics · March 2003
We analyze a mathematical model of paced cardiac muscle consisting of a map relating the duration of an action potential to the preceding diastolic interval as well as the preceding action potential duration, thereby containing some degree of "memory." The ...
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Journal ArticleChaos (Woodbury, N.Y.) · December 2002
The Fenton-Karma model is a simplification of complex ionic models of cardiac membrane that reproduces quantitatively many of the characteristics of heart cells; its behavior is simple enough to be understood analytically. In this paper, a map is derived t ...
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Journal ArticleThe European physical journal. E, Soft matter · April 2002
A theory of stress fields in two-dimensional granular materials based on directed force chain networks is presented. A general Boltzmann equation for the densities of force chains in different directions is proposed and a complete solution is obtained for ...
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