FIG. 4.

Spatiotemporal dynamics of the 2D stochastic map at steady state. The system is initialized with uniform initial conditions with $x_{ij}(0)=1$. (a) Coupling strength is set to $l=2$, and the system is paced at $T=650\mathrm{ms}$ corresponding to the P1 case. Snapshots of the system after 1000 beats show that steady state Ca is spatially uniform with small fluctuations. Color bar indicates the local SR load $x_{ij}$. The probability density plotted to the right captures the distribution of $x_{ij}$ at steady state and shows that it is sharply peaked in the range [0.7–0.8]. (b) The system is paced at $T=450\mathrm{ms}$ corresponding to the period 2 regime. The SR load is spatially uniform at steady state with the distribution showing two peaks in the range [0.55–0.60] and near 0.75. (c) At $T=275\mathrm{ms}$, the system exhibits global period 1 behavior as in the case for $T=650\mathrm{ms}$ although the system is spatially disordered. (d) Increasing the spatial coupling to $l=8$ and pacing the system at $T=270\mathrm{ms}$ yield period 3 behavior. The SR load is effectively spatially uniform at each beat and the steady state $x_{ij}$ is distributed around 3 distinct peaks.