Nonlinear dynamics of a mathematical model on action potential duration and calcium transient in paced cardiac cells

Jiying Ma; Dongmei Xiao

doi:10.3934/dcdsb.2013.18.2377

Article Contents

2013, Volume 18, Issue 9: 2377-2396. Doi: 10.3934/dcdsb.2013.18.2377

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Nonlinear dynamics of a mathematical model on action potential duration and calcium transient in paced cardiac cells

Jiying Ma^1, and
Dongmei Xiao^2,

1.
Department of Mathematics, MOE-LSC, Shanghai Jiao Tong University, Shanghai, 200240
2.
Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240

Received: June 30, 2012

Revised: July 31, 2013

Published: October 2013

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Abstract

In the paper we focus on the dynamics of a two-dimensional discrete-time mathematical model, which describes the interaction between the action potential duration (APD) and calcium transient in paced cardiac cells. By qualitative and bifurcation analysis, we prove that this model can undergo period-doubling bifurcation and Neimark-Sacker bifurcation as parameters vary, respectively. These results provide theoretical support on some experimental observations, such as the alternans of APD and calcium transient, and quasi-periodic oscillations between APD and calcium transient in paced cardiac cells. The rich and complicated bifurcation phenomena indicate that the dynamics of this model are very sensitive to some parameters, which might have important implications for the control of cardiovascular disease.

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Mathematics Subject Classification: Primary: 37E05, 37G10; Secondary: 92B05.

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