On conditions for qualitative instability of regulatory circuits with applications to immunological control loops. (English) Zbl 0585.92008
Mathematics and computers in biomedical applications, Proc. IMACS Conf., 39-53 (1985).
[For the entire collection see Zbl 0559.00026.]
The immune system’s many interacting cell types have lead to many models trying to describe and characterize their interactions. Here, the authors present a fairly easy way to analyze the stability of such networks almost immediately from diagrams of the interactions. Of special interest are analyses of models proposed by Herzenberg et al, the second author, Richter, and Hiernaux. All are found to have deficiencies. The work is similar in spirit to that of B. L. Clarke on using graph theory to predict stability of chemical networks [J. Chem. Phys. 60, 1493-1501 (1974) and ibid. 62, 773-775 (1975)].
The immune system’s many interacting cell types have lead to many models trying to describe and characterize their interactions. Here, the authors present a fairly easy way to analyze the stability of such networks almost immediately from diagrams of the interactions. Of special interest are analyses of models proposed by Herzenberg et al, the second author, Richter, and Hiernaux. All are found to have deficiencies. The work is similar in spirit to that of B. L. Clarke on using graph theory to predict stability of chemical networks [J. Chem. Phys. 60, 1493-1501 (1974) and ibid. 62, 773-775 (1975)].
Reviewer: S.J.Merrill
MSC:
| 92C50 | Medical applications (general) |
| 92Cxx | Physiological, cellular and medical topics |
| 05C75 | Structural characterization of families of graphs |
| 34D99 | Stability theory for ordinary differential equations |
| 94C99 | Circuits, networks |
| 93C15 | Control/observation systems governed by ordinary differential equations |
| 93D20 | Asymptotic stability in control theory |
