FIG. 4.

Synchronization of Ca–spatially discordant alternans (SDA) to action potential duration (APD)-SDA patterns in the amplitude equation (AE) model without Ca-to-APD coupling $(\gamma =0)$. (a) Plots of function $f\left(\mathrm{\Delta }c\right)$ [Eq. (12)] for different $\sigma \mathrm{\Delta }a$ values. (b) Space-time plots of $\mathrm{\Delta }c$ for $\sigma =0.1$ (left) and $\sigma =0.5$ (right) for a one-node APD-SDA as indicated. (c) Space-time plots of $\mathrm{\Delta }c$ for $\sigma =0.1$ with two noise strengths: $D=500$ (left) and $D=1000$ (right). (d) $S_{vc}$ vs noise strength $D$. For each $D$, 20 simulations with different random initial conditions are carried out with the corresponding $S_{vc}$ plotted. In the simulations in (b)-(d), the initial conditions for Ca-SDA are spatially random in which $\mathrm{\Delta }c$ is a binary number, randomly chosen as either −100 or 100. $\mathrm{\Delta }a$ is a one-node SDA as indicated in (b). $\alpha =0.5$ and $\rho =0.5$.