Further remarks on delay dynamics in Oregonator models
暂无分享,去创建一个
Silviu-Iulian Niculescu | Islam Boussaada | Hakki Ulas Ünal | Hakki Ulaş Ünal | S. Niculescu | I. Boussaada
[1] Irving R. Epstein,et al. Differential delay equations in chemical kinetics. Nonlinear models: The cross‐shaped phase diagram and the Oregonator , 1991 .
[2] Silviu-Iulian Niculescu,et al. Tracking the Algebraic Multiplicity of Crossing Imaginary Roots for Generic Quasipolynomials: A Vandermonde-Based Approach , 2016, IEEE Transactions on Automatic Control.
[3] S. Niculescu. Delay Effects on Stability: A Robust Control Approach , 2001 .
[4] R. M. Noyes,et al. Oscillations in chemical systems. IV. Limit cycle behavior in a model of a real chemical reaction , 1974 .
[5] Lars Folke Olsen,et al. Biochemical oscillations and cellular rhythms: The molecular bases of periodic and chaotic behaviour: Albert Goldbeter. Cambridge University Press, Cambridge, 1996. $99.95 (cloth), 605 + xxiv pp , 1997 .
[6] S H Strogatz,et al. Coupled oscillators and biological synchronization. , 1993, Scientific American.
[7] Irving R. Epstein,et al. Delay effects and differential delay equations in chemical kinetics , 1992 .
[8] Silviu-Iulian Niculescu,et al. Characterizing the Codimension of Zero Singularities for Time-Delay Systems , 2016, Acta Applicandae Mathematicae.
[9] J. Hopfield,et al. From molecular to modular cell biology , 1999, Nature.
[10] Rifat Sipahi,et al. An exact method for the stability analysis of time-delayed linear time-invariant (LTI) systems , 2002, IEEE Trans. Autom. Control..
[11] B. Goodwin. Oscillatory behavior in enzymatic control processes. , 1965, Advances in enzyme regulation.
[12] Jack K. Hale,et al. Introduction to Functional Differential Equations , 1993, Applied Mathematical Sciences.
[13] J. Guckenheimer,et al. Defining Functions for Multiple Hopf Bifurcations , 1997 .
[14] Frank Allgöwer,et al. Stability Analysis for Time-Delay Systems using Rekasius's Substitution and Sum of Squares , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.
[15] Hakki Ulaş Ünal,et al. A Delay-Based Sustained Chemical Oscillator: Qualitative Analysis of Oregonator-Based Models , 2017, IEEE Life Sciences Letters.
[16] M. Roussel. The Use of Delay Differential Equations in Chemical Kinetics , 1996 .
[17] E D Sontag,et al. Some new directions in control theory inspired by systems biology. , 2004, Systems biology.
[18] Dirk Roose,et al. Numerical bifurcation analysis of delay differential equations using DDE-BIFTOOL , 2002, TOMS.
[19] Jie Chen,et al. On stability crossing curves for general systems with two delays , 2004 .