TY - GEN
T1 - Determining the structural properties of a class of biological models
AU - Blanchini, Franco
AU - Franco, Elisa
AU - Giordano, Giulia
PY - 2012/12/1
Y1 - 2012/12/1
N2 - A property for a class of systems is said to be structural if it is met by any system in the class regardless of the adopted parameters. In this paper we investigate the structural nature of oscillatory behaviors, adaptation and monotonicity in a class of sign-invariant systems, capturing a wide variety of biological models. We employ standard robustness analysis tools, suitably tailored to the category of sign definite dynamics, i.e. in which terms are monotonic with respect to all arguments. In particular, our results are based on Jacobian analysis and invariant sets, and we are able to provide simple criteria to determine whether a system structurally admits Hopf-type bifurcations, perfect adaptation or monotonic behavior. Such criteria are easily verified numerically on a set of examples.
AB - A property for a class of systems is said to be structural if it is met by any system in the class regardless of the adopted parameters. In this paper we investigate the structural nature of oscillatory behaviors, adaptation and monotonicity in a class of sign-invariant systems, capturing a wide variety of biological models. We employ standard robustness analysis tools, suitably tailored to the category of sign definite dynamics, i.e. in which terms are monotonic with respect to all arguments. In particular, our results are based on Jacobian analysis and invariant sets, and we are able to provide simple criteria to determine whether a system structurally admits Hopf-type bifurcations, perfect adaptation or monotonic behavior. Such criteria are easily verified numerically on a set of examples.
UR - http://www.scopus.com/inward/record.url?scp=84874235509&partnerID=8YFLogxK
U2 - 10.1109/CDC.2012.6427037
DO - 10.1109/CDC.2012.6427037
M3 - Conference contribution
AN - SCOPUS:84874235509
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 5505
EP - 5510
BT - Proceedings of the IEEE Conference on Decision and Control
ER -