NONLINEAR DYNAMICS OF A MATHEMATICAL MODEL ON ACTION POTENTIAL DURATION AND CALCIUM TRANSIENT IN PACED CARDIAC CELLS

作者：Ma, Jiying; Xiao, Dongmei^*

来源：Discrete and Continuous Dynamical Systems-Series B, 2013, 18(9): 2377-2396.

DOI：10.3934/dcdsb.2013.18.2377

• Discrete-time mathematical model
• APD restitution
• calcium transient
• period-doubling bifurcation
• Neimark-Sacker bifurcation

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.

• 出版日期2013-11
• 单位上海交通大学