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Excitability in a model with a saddlenode homoclinic bifurcation
Modeling the intravenous glucose tolerance test: A global study for a singledistributeddelay model
1.  Centre for Cellular and Molecular Biology, Hyderabad  500 007, India 
2.  BioMath Lab, CNR IASI Fisiopatologia Shock UCSC, L.go A. Gemelli, 8  00168 Roma, Italy 
3.  IRD Bondy et Université de Pau, Paris, France 
[1] 
Pasquale Palumbo, Simona Panunzi, Andrea De Gaetano. Qualitative behavior of a family of delaydifferential models of the GlucoseInsulin system. Discrete & Continuous Dynamical Systems  B, 2007, 7 (2) : 399424. doi: 10.3934/dcdsb.2007.7.399 
[2] 
Jiaxu Li, Yang Kuang, Bingtuan Li. Analysis of IVGTT glucoseinsulin interaction models with time delay. Discrete & Continuous Dynamical Systems  B, 2001, 1 (1) : 103124. doi: 10.3934/dcdsb.2001.1.103 
[3] 
Tomás Caraballo, Francisco Morillas, José Valero. On differential equations with delay in Banach spaces and attractors for retarded lattice dynamical systems. Discrete & Continuous Dynamical Systems  A, 2014, 34 (1) : 5177. doi: 10.3934/dcds.2014.34.51 
[4] 
Ismael Maroto, Carmen NÚÑez, Rafael Obaya. Dynamical properties of nonautonomous functional differential equations with statedependent delay. Discrete & Continuous Dynamical Systems  A, 2017, 37 (7) : 39393961. doi: 10.3934/dcds.2017167 
[5] 
Neville J. Ford, Stewart J. Norton. Predicting changes in dynamical behaviour in solutions to stochastic delay differential equations. Communications on Pure & Applied Analysis, 2006, 5 (2) : 367382. doi: 10.3934/cpaa.2006.5.367 
[6] 
Saloni Rathee, Nilam. Quantitative analysis of time delays of glucose  insulin dynamics using artificial pancreas. Discrete & Continuous Dynamical Systems  B, 2015, 20 (9) : 31153129. doi: 10.3934/dcdsb.2015.20.3115 
[7] 
Bin Wang, Arieh Iserles. Dirichlet series for dynamical systems of firstorder ordinary differential equations. Discrete & Continuous Dynamical Systems  B, 2014, 19 (1) : 281298. doi: 10.3934/dcdsb.2014.19.281 
[8] 
Pham Huu Anh Ngoc. Stability of nonlinear differential systems with delay. Evolution Equations & Control Theory, 2015, 4 (4) : 493505. doi: 10.3934/eect.2015.4.493 
[9] 
Michael Dellnitz, Mirko HesselVon Molo, Adrian Ziessler. On the computation of attractors for delay differential equations. Journal of Computational Dynamics, 2016, 3 (1) : 93112. doi: 10.3934/jcd.2016005 
[10] 
Hermann Brunner, Stefano Maset. Time transformations for delay differential equations. Discrete & Continuous Dynamical Systems  A, 2009, 25 (3) : 751775. doi: 10.3934/dcds.2009.25.751 
[11] 
Klaudiusz Wójcik, Piotr Zgliczyński. Topological horseshoes and delay differential equations. Discrete & Continuous Dynamical Systems  A, 2005, 12 (5) : 827852. doi: 10.3934/dcds.2005.12.827 
[12] 
A. Domoshnitsky. About maximum principles for one of the components of solution vector and stability for systems of linear delay differential equations. Conference Publications, 2011, 2011 (Special) : 373380. doi: 10.3934/proc.2011.2011.373 
[13] 
Evelyn Buckwar, Girolama Notarangelo. A note on the analysis of asymptotic meansquare stability properties for systems of linear stochastic delay differential equations. Discrete & Continuous Dynamical Systems  B, 2013, 18 (6) : 15211531. doi: 10.3934/dcdsb.2013.18.1521 
[14] 
Yejuan Wang, Lin Yang. Global exponential attraction for multivalued semidynamical systems with application to delay differential equations without uniqueness. Discrete & Continuous Dynamical Systems  B, 2017, 22 (11) : 127. doi: 10.3934/dcdsb.2018257 
[15] 
María J. Garrido–Atienza, Kening Lu, Björn Schmalfuss. Random dynamical systems for stochastic partial differential equations driven by a fractional Brownian motion. Discrete & Continuous Dynamical Systems  B, 2010, 14 (2) : 473493. doi: 10.3934/dcdsb.2010.14.473 
[16] 
Serhiy Yanchuk, Leonhard Lücken, Matthias Wolfrum, Alexander Mielke. Spectrum and amplitude equations for scalar delaydifferential equations with large delay. Discrete & Continuous Dynamical Systems  A, 2015, 35 (1) : 537553. doi: 10.3934/dcds.2015.35.537 
[17] 
Nicola Guglielmi, Christian Lubich. Numerical periodic orbits of neutral delay differential equations. Discrete & Continuous Dynamical Systems  A, 2005, 13 (4) : 10571067. doi: 10.3934/dcds.2005.13.1057 
[18] 
Eduardo Liz, Gergely Röst. On the global attractor of delay differential equations with unimodal feedback. Discrete & Continuous Dynamical Systems  A, 2009, 24 (4) : 12151224. doi: 10.3934/dcds.2009.24.1215 
[19] 
Alfonso RuizHerrera. Chaos in delay differential equations with applications in population dynamics. Discrete & Continuous Dynamical Systems  A, 2013, 33 (4) : 16331644. doi: 10.3934/dcds.2013.33.1633 
[20] 
Leonid Berezansky, Elena Braverman. Stability of linear differential equations with a distributed delay. Communications on Pure & Applied Analysis, 2011, 10 (5) : 13611375. doi: 10.3934/cpaa.2011.10.1361 
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