MicroRNAs and Robustness in Biological Regulatory Networks. A Generic Approach with Applications at Different Levels: Physiologic, Metabolic, and Genetic - Systems Biology of Metabolic and Signaling Networks - page 67

µ=0.4

µ=0.04

µ=0.6

x 2

µ=1

µ=4

x 1

Fig. 4.3 Top: Dynamical system with the Hamiltonian and potential surfaces H and P , showing a
revolution symmetry and sharing contour lines, especially the limit cycle C of the dynamical
system ( in green ). Middle : simulations of van der Pol system d x 1 /d t ¼ x 2 ,d x 2 /d t ¼x 1 +
μ (1 x 1 2 ) x 2 , for different values of the bifurcating anharmonic parameter μ ( http://www.
sciencesunivnantesfr_sites_genevieve_tulloue_index_fichiers_animflash.html ) . At the center, we
have a representation of the velocity field for μ ¼ 0.6. Bottom : fit between the isolated cardiac cell
rhythm ( in white ) and the solution of the van der Pol system ( in blue )

4.3.4 Example of a Mixed Principal Potential Part Metabolic
Network in High Glycolysis

The upper part of glycolysis contains two key enzymes, the PhosphoFructo-
Kinase (PFK), which can be considered as following a Hill kinetics of order n ,
and the Aldolase, which follows a parabolic Hill (Demongeot and Doncescu