Systems Biology (Methods in Molecular Biology)

For the critical valueI3.71 it appears as a phase transition of

the type “first-order” through a supercritical Andronov-Hopf

bifurcation as described in [24, 52], giving rise to a limit cycle,

periodic oscillations, and self-organizing system outside the ther-

modynamic equilibrium. It is further noted as the maximum con-

centration values of the population of proliferating tumor cells

increase significantly.

It is noteworthy, as can be seen in Fig.4, as far as it decreases

the value of the control parameterI, although the system exhibits

8

7

6

5

mmol/ml^4

mmol/ml mmol/ml

mmol/ml

mmol/ml mmol/ml

3

2

1

0

7

12

10

8

6

4

2

0

6 5 4 3 2 1 0

10

8

6

4

2

0

10

8

6

4

2

0

12

8

10

6

4

2

0

050

C

AB

D

100

s

150 200

0

E F

50 100

s

150 200 0 50 100

s

150 200

0 50 100

s

150 200

0 50 100

s

0 50 100 150 200

s

150 200

Fig. 4Dynamical behavior of the proposed model (Eq.24) for different values of the control parameter
I(N¼5,H¼3): (a) stationary state (I¼4), (b) limit cycle (I¼3), (c) limit cycle (I¼2), (d) limit cycle
(I¼1), (e) limit cycle (I¼0.7), (f) chaos (I¼0.4);red(x),blue(y) andgreen(z). Reprinted from [83]

140 Sheyla Montero et al.