Systems Biology (Methods in Molecular Biology)

periodic oscillations, the maximum concentration of z cells

increases, and in fact they become predominant.

From the control parametersI0.65 a cascade of bifurcations

is triggered by the route of saddle-focus Shilnikov’s bifurcation

[59] and even when the maximum values of the population of

proliferating tumor cells decrease, the prevalence of metastatic

cellszcontinues.

It shows how, for lower outcomes of the critical value of the

control parameter (seeTable1,I¼0.4 and Fig.4f), related to

immune surveillance, tumor cells exhibit random behavior, as Shil-

nikov’s chaos [59](seeattractor and return map in Fig.5).

3.5

5

Xmax vs Previous Xmax

Previous X

X

0

05

2.5

2

1.5

0.5

(^12)
(^34)
(^56)
(^78)
9 0
0.5
1
1.5
2
2.5
3
[X]t
[Z]t
[Y]t
3.5
4
4.5
0
1
3
Fig. 5Chaotic attractor and return map obtained from Eq. (19), withI¼0.4. Reprinted from [83]
Parameters Estimation in Phase-Space Landscape Reconstruction of Cell Fate... 141