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10.25.2013: Z-P system with spatial nonuniformity with and without diffusion

Here, we study the evolution of a patch of Z and P initially at equilibrium (at least at the center of the patch) without (case #1) and with (case #2) diffusion.

In the first case, at the center of the patch, the Z and P values are exactly at equilibrium and they do not vary in time (not shown). Just off that center, however, the slight disequilibrium results in a periodic response (Fig. 1). This periodic response is active everywhere inside the initial patch (except right at the center) with the patch not increasing in size with time in the absence of diffusion (Figs.2 and 3).

The evolution of the system in the presence of diffusion is similar except that: 1. Z and P at the center are not anymore time independent but also vary periodically (not shown). 2. The patch where Z and P vary periodically in time increases slowly in size (Figs. 5 and 6). 6. Outside that patch, P abruptly shifts from zero to 1 and this shifts also spreads outward at a speed faster than the speed at which the Z-P patch spreads (Figs. 5 and 6). The speed of that shift (300 days to do 20 km) appears to be the same than in the V-P case (Fig. 5 in 10.22.2013: First runs with spatial nonuniformity with and without diffusion. Part 2).

Case #1

../../../../../../_images/equilibrium_3_diffk_0_timeseries.png

Figure 1: Time series in case #1.

../../../../../../_images/equilibrium_3_diffk_0_snapshots.png

Figure 2: Snapshots in case #1.

../../../../../../_images/equilibrium_3_diffk_0_yt_section.png

Figure 3: Time series of Ps along x=50 km in case #1.

Case #2

../../../../../../_images/equilibrium_2_diffk_37_99_timeseries.png

Figure 4: Time series in case #2.

../../../../../../_images/equilibrium_2_diffk_37_99_snapshots.png

Figure 5: Snapshots in case #2.

../../../../../../_images/equilibrium_2_diffk_37_99_yt_section.png

Figure 6: Time series of Ps along x=50 km in case #2.


Snapshots, time series and y-t section figures are plotted with plot_snapshot_current_run.py, plot_timeseries_current_run.py and plot_yt_section_current_run.py in RESEARCH/MODELISATION/marine_viruses/current_version/runs/run_002/analysis/ on ipu1.