  Kick synchronization versus diffusive synchronizationMauroy, Alexandre  ; Sacré, Pierre ; Sepulchre, Rodolphe in Proceedings of the 51st IEEE Conference on Decision and Control (2012, December) The paper provides an introductory discussion about two fundamental models of oscillator synchronization: the (continuous-time) diffusive model, that dominates the mathematical literature on ... [more ▼] The paper provides an introductory discussion about two fundamental models of oscillator synchronization: the (continuous-time) diffusive model, that dominates the mathematical literature on synchronization, and the (hybrid) kick model, that accounts for most popular examples of synchronization, but for which only few theoretical results exist. The paper stresses fundamental differences between the two models, such as the different contraction measures underlying the analysis, as well as important analogies that can be drawn in the limit of weak coupling. [less ▲] Detailed reference viewed: 4 (0 ULg)Metrics for oscillator models: an input-to-phase approachSacré, Pierre ; Sepulchre, Rodolphe Conference (2012, March) Detailed reference viewed: 62 (21 ULg)Matching an oscillator model to a phase response curveSacré, Pierre ; Sepulchre, Rodolphe in Proceedings of the Joint 50th IEEE Conference on Decision and Control and European Control Conference (2011, December) The Phase Response Curve (PRC) has proven a useful tool for the reduction of complex oscillator models. It is also an information often experimentally available to the biologist. This paper introduces a ... [more ▼] The Phase Response Curve (PRC) has proven a useful tool for the reduction of complex oscillator models. It is also an information often experimentally available to the biologist. This paper introduces a numerical tool based on the sensitivity analysis of the PRC to adapt initial model parameters in order to match a particular PRC shape. We illustrate the approach on a simple biochemical model of circadian oscillator. [less ▲] Detailed reference viewed: 43 (14 ULg)Sensitivity analysis of phase response curvesSacré, Pierre ; Sepulchre, Rodolphe Conference (2011, May 23) The Phase Response Curve (PRC) has proven a useful tool for the reduction of complex oscillator models to one-dimensional phase models. We introduce the sensitivity analysis of this important mathematical ... [more ▼] The Phase Response Curve (PRC) has proven a useful tool for the reduction of complex oscillator models to one-dimensional phase models. We introduce the sensitivity analysis of this important mathematical object and its numerical implementation. As an application, we study simple biochemical models of circadian oscillators and discuss how sensitivity analysis helps drawing connections between the state-space model of the oscillator and its phase response curve. [less ▲] Detailed reference viewed: 64 (20 ULg)Sensitivity analysis of phase response curvesSacré, Pierre ; Sepulchre, Rodolphe Conference (2011, March 16) Detailed reference viewed: 34 (15 ULg)Multiple feedback loops in circadian cycles: robustness and entrainment as selection criteria; Sacré, Pierre ; et alin Proceedings of the Seventh International Workshop on Computational Systems Biology, WCSB 2010 (2010, June) This paper discusses the contribution of an additional feedback loop to the entrainment and the robustness of a circadian system. To quantify robustness, we perform a global analysis of the system's ... [more ▼] This paper discusses the contribution of an additional feedback loop to the entrainment and the robustness of a circadian system. To quantify robustness, we perform a global analysis of the system's parameter space. We quantify the parameter region where the circuit displays an experimentally observed behavior, under entrainment. This global measure is comleted with a classification based on the phase response curve (PRC). For two models of circadian rhythms, we found that the one with two loops is more robust than the one with a single loop: the two-loop model shows better resilience to parameter perturbations and it has also a larger region where the PRC matches experimental PRCs of circadian oscillators. [less ▲] Detailed reference viewed: 88 (36 ULg)Selection of circadian clock models for robust entrainment: an analysis based on the phase response curveSacré, Pierre ; ; et alConference (2010, March 30) Detailed reference viewed: 50 (27 ULg)Controlling the phase of an oscillator: a phase response curve approach; Sacré, Pierre ; Sepulchre, Rodolphe in Proceedings of the Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference (2009, December) The paper discusses elementary control strategies to control the phase of an oscillator. Both feedforward and feedback (P and PI) control laws are designed based on the phase response curve (PRC ... [more ▼] The paper discusses elementary control strategies to control the phase of an oscillator. Both feedforward and feedback (P and PI) control laws are designed based on the phase response curve (PRC) calculated from the linearized model. The performance is evaluated on a popular model of circadian oscillations. [less ▲] Detailed reference viewed: 78 (55 ULg)On the influence of positive and negative feedback loops on the phase response curve of biological oscillators.Sacré, Pierre ; Sepulchre, Rodolphe Conference (2009, March) Detailed reference viewed: 89 (34 ULg) |
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