Non linear control

We continue the previous experiment . where three CA exchange resources (age). None is injured, yet CA-1 differentiates.  When its cells reach  max age = 110, their age is set to zero and they are secreted into the environment. CA-1 differentiation initiates  cell production. The present experiment explores how the exchange of resources in the system affects cell production.

The first graph on the left depicts ages of three isolated, non interacting CA. They continually accumulate age (resources) the spikes result from the loss of peripheral cells. The graph to its right  depicts the total age (resources) of the system.

In the second  experiment  max  age of CA-1 was set to 110 (compare with ch-61). Initially all cells were younger than max age. Somewhat later, they reached max age and   their age was set to zero. These cells were then secreted into the environment. All together, during this experiment, CA-1 produced 15 cells.  The other two CA aged as above.

In the third experiment.  CA-2 contributed its resources to CA-1 whereupon CA-1 started deteriorating and died at t = 20. It produced 11 cells.  The same outcome was observed when  both CA-1 and CA-2 exchanged resources.

In the  fourth experiment below,  CA-3 contributed its resources. The system started oscillating and produced 35 cells

In the last experiment,  resources were freely distributed between all CA. Nevertheless CA-1 died after producing 13 cells. CA-2 and CA-3 remained alive yet their resources (ages) were completely depleted.

Aging velocity
The amount of resources produced by a CA depends on its aging velocity. As CA transfers its  resources its aging  decelerates.

Health is  defined here as production / total age. Apparently  the system tested in the fourth experiment was the healthiest.

The behavior of this simple system beats any intuition. One would expect that adding resources to CA-1, like in the second experiment , might be beneficial, nonetheless CA-1 died.  The response is unpredictable. In small systems one might  evaluate all possible links between the CA. and find an  optimal configuration. (solution). With a larger CA set such  is unthinkable, and may not be necessary. Why not let the system itself  come up with its optimal solution?

Setup
nca=3;  zygote -> effect[no 1000]; go109];  restoreparams; effect[1, 110, 0];  support[ *, *];  go [100];

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