This work deals with the stimulation of cardiac spiral waves in a two-dimensional FitzHugh–Nagumo model through modulational instability phenomenon in the presence of intracellular magnetic flux. The nonlinear generic model is firstly transformed into a two-dimensional complex Ginzburg–Landau equation with a small real damping term. Then, the latter is explored to perform the linear stability analysis and some modulational instability properties are derived and found to be modified with the change of either the magnetic coupling strength or the diffusion coefficient which are set as the control parameters. The bifurcation theory analysis is numerically performed, and the range of values of the stimulation parameter for which firing patterns emerge in cardiac media is well estimated. The recording of membrane potential as well as the magnetic flux as functions of time or spatial coordinates allows to picture some features such as time series, phase portraits and spatial patterns of membrane potential. As a result, diamond-shaped, squared-shaped and spiral-shaped waves are obtained. An elimination process of multi-spiral waves is proposed by exposing such patterns to an external magnetic flux. Thus, for suited values of parameters, the cardiac spiral waves are transmuted into target waves which obviously protect heart against harmful attacks such as ventricular tachycardia and fibrillation. Our results suggest that uncontrolled electromagnetic induction within cardiac tissue may be considered as the principal source of many heart injuries which are the first cause of mortality in the industrial world.

这项工作通过存在细胞内磁通量的调制不稳定性现象来处理二维FitzHugh-Nagumo模型中的心脏螺旋波的刺激。首先将非线性通用模型转换为具有较小实际阻尼项的二维复Ginzburg-Landau方程。然后，探索后者以进行线性稳定性分析，并得出一些调制不稳定性，并发现其随设置为控制参数的磁耦合强度或扩散系数的变化而被修改。对分叉理论进行数值分析，并且可以很好地估计出在心脏介质中出现放电模式的刺激参数值的范围。膜电位以及磁通量作为时间或空间坐标的函数的记录允许描绘一些特征，例如时间序列，相画像和膜电位的空间模式。结果，获得菱形，正方形和螺旋形的波。通过将这样的图案暴露于外部磁通量，提出了消除多螺旋波的方法。因此，对于合适的参数值，心脏螺旋波被转换为目标波，从而明显保护心脏免受有害攻击，例如心室心动过速和心律颤动。我们的研究结果表明，心脏组织内不受控制的电磁感应可能被认为是许多心脏损伤的主要来源，这是工业界造成死亡的首要原因。