DCDS-B
Nonlinear dynamics of a mathematical model on action potential duration and calcium transient in paced cardiac cells
Jiying Ma Dongmei Xiao
Discrete & Continuous Dynamical Systems - B 2013, 18(9): 2377-2396 doi: 10.3934/dcdsb.2013.18.2377
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.
keywords: period-doubling bifurcation Discrete-time mathematical model APD restitution Neimark-Sacker bifurcation. calcium transient
DCDS
Monotonicity, asymptotics and uniqueness of travelling wave solution of a non-local delayed lattice dynamical system
Zhaoquan Xu Jiying Ma
Discrete & Continuous Dynamical Systems - A 2015, 35(10): 5107-5131 doi: 10.3934/dcds.2015.35.5107
A delayed lattice dynamical system with non-local diffusion and interaction is considered in this paper. The exact asymptotics of the wave profile at both wave tails is derived, and all the wave profiles are shown to be strictly increasing. Moreover, we prove that the wave profile with a given admissible speed is unique up to translation. These results generalize earlier monotonicity, asymptotics and uniqueness results in the literature.
keywords: non-local diffusion and interaction. asymptotics uniqueness delayed lattice dynamical system monotonicity Travelling waves

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