Geometric ideas in the stability analysis of delay models in biosciences

Silviu-Iulian Niculescu (1) , Irinel-Constantin Morarescu (2) , Wim Michiels (3) , Keqin Gu (4)

1 L2S - Laboratoire des signaux et systèmes
2 UPB - Universitatea Politehnica din Bucuresti [Bucarest, Roumanie]
3 KU Leuven - Catholic University of Leuven = Katholieke Universiteit Leuven
4 Illinois State University

This chapter focuses on the stability analysis of various continuous-time delay systems encountered in biosciences. Our main interest is to characterize the effects induced by the presence of delays on the systems' stability. More precisely, we present some intuitive and easy to follow geometric ideas for characterizing the behavior of the characteristic roots (or eigenvalues) of the corresponding linearized models with respect to the imaginary axis for the single and multiple discrete (constant) delays or for some particular classes of distributed delays (gamma-distribution with a gap). Several examples (human respiration, cell-to-cell spread models in well-mixed configurations or immune dynamics in chronic leukemia) complete the presentation.

Mots clés: robustness; stabilization; delay

Domaines: Automatique

Silviu-Iulian Niculescu, Irinel-Constantin Morarescu, Wim Michiels, Keqin Gu. Geometric ideas in the stability analysis of delay models in biosciences. Queinnec, I; Tarbouriech, S; Garcia, G; Niculescu, SI. Biology and Control Theory: Current Challenges, 357, SPRINGER-VERLAG BERLIN, 2007, Lecture Notes in Control and Information Sciences book series (LNCIS), ⟨10.1007/978-3-540-71988-5_10⟩. ⟨hal-02194455⟩