 Previous Article
 MBE Home
 This Issue

Next Article
A finite element method for growth in biological development
Delay differential equations via the matrix lambert w function and bifurcation analysis: application to machine tool chatter
1.  Department of Mechanical Engineering, University of Michigan, 2350 Hayward Street, Ann Arbor, MI 481092125, United States, United States 
2.  Department of Mathematics, University of Michigan, 525 East University, Ann Arbor, MI 481091109, United States 
[1] 
Ábel Garab. Unique periodic orbits of a delay differential equation with piecewise linear feedback function. Discrete & Continuous Dynamical Systems  A, 2013, 33 (6) : 23692387. doi: 10.3934/dcds.2013.33.2369 
[2] 
Tomás Caraballo, Renato Colucci, Luca Guerrini. Bifurcation scenarios in an ordinary differential equation with constant and distributed delay: A case study. Discrete & Continuous Dynamical Systems  B, 2019, 24 (6) : 26392655. doi: 10.3934/dcdsb.2018268 
[3] 
Josef Diblík, Zdeněk Svoboda. Asymptotic properties of delayed matrix exponential functions via Lambert function. Discrete & Continuous Dynamical Systems  B, 2018, 23 (1) : 123144. doi: 10.3934/dcdsb.2018008 
[4] 
Rui Hu, Yuan Yuan. Stability, bifurcation analysis in a neural network model with delay and diffusion. Conference Publications, 2009, 2009 (Special) : 367376. doi: 10.3934/proc.2009.2009.367 
[5] 
Runxia Wang, Haihong Liu, Fang Yan, Xiaohui Wang. Hopfpitchfork bifurcation analysis in a coupled FHN neurons model with delay. Discrete & Continuous Dynamical Systems  S, 2017, 10 (3) : 523542. doi: 10.3934/dcdss.2017026 
[6] 
Fengqi Yi, Eamonn A. Gaffney, Sungrim SeirinLee. The bifurcation analysis of turing pattern formation induced by delay and diffusion in the Schnakenberg system. Discrete & Continuous Dynamical Systems  B, 2017, 22 (2) : 647668. doi: 10.3934/dcdsb.2017031 
[7] 
P. Dormayer, A. F. Ivanov. Symmetric periodic solutions of a delay differential equation. Conference Publications, 1998, 1998 (Special) : 220230. doi: 10.3934/proc.1998.1998.220 
[8] 
Eugen Stumpf. Local stability analysis of differential equations with statedependent delay. Discrete & Continuous Dynamical Systems  A, 2016, 36 (6) : 34453461. doi: 10.3934/dcds.2016.36.3445 
[9] 
Hasib Khan, Cemil Tunc, Aziz Khan. Green function's properties and existence theorems for nonlinear singulardelayfractional differential equations. Discrete & Continuous Dynamical Systems  S, 2018, 0 (0) : 00. doi: 10.3934/dcdss.2020139 
[10] 
Yuncherl Choi, Jongmin Han, ChunHsiung Hsia. Bifurcation analysis of the damped KuramotoSivashinsky equation with respect to the period. Discrete & Continuous Dynamical Systems  B, 2015, 20 (7) : 19331957. doi: 10.3934/dcdsb.2015.20.1933 
[11] 
Toshiyuki Ogawa, Takashi Okuda. Bifurcation analysis to SwiftHohenberg equation with Steklov type boundary conditions. Discrete & Continuous Dynamical Systems  A, 2009, 25 (1) : 273297. doi: 10.3934/dcds.2009.25.273 
[12] 
Fang Han, Bin Zhen, Ying Du, Yanhong Zheng, Marian Wiercigroch. Global Hopf bifurcation analysis of a sixdimensional FitzHughNagumo neural network with delay by a synchronized scheme. Discrete & Continuous Dynamical Systems  B, 2011, 16 (2) : 457474. doi: 10.3934/dcdsb.2011.16.457 
[13] 
Zuolin Shen, Junjie Wei. Hopf bifurcation analysis in a diffusive predatorprey system with delay and surplus killing effect. Mathematical Biosciences & Engineering, 2018, 15 (3) : 693715. doi: 10.3934/mbe.2018031 
[14] 
Jinhu Xu, Yicang Zhou. Bifurcation analysis of HIV1 infection model with celltocell transmission and immune response delay. Mathematical Biosciences & Engineering, 2016, 13 (2) : 343367. doi: 10.3934/mbe.2015006 
[15] 
Ming Liu, Dongpo Hu, Fanwei Meng. Stability and bifurcation analysis in a delayinduced predatorprey model with MichaelisMenten type predator harvesting. Discrete & Continuous Dynamical Systems  S, 2018, 0 (0) : 00. doi: 10.3934/dcdss.2020259 
[16] 
Michael Scheutzow. Exponential growth rate for a singular linear stochastic delay differential equation. Discrete & Continuous Dynamical Systems  B, 2013, 18 (6) : 16831696. doi: 10.3934/dcdsb.2013.18.1683 
[17] 
BaoZhu Guo, LiMing Cai. A note for the global stability of a delay differential equation of hepatitis B virus infection. Mathematical Biosciences & Engineering, 2011, 8 (3) : 689694. doi: 10.3934/mbe.2011.8.689 
[18] 
Arne Ogrowsky, Björn Schmalfuss. Unstable invariant manifolds for a nonautonomous differential equation with nonautonomous unbounded delay. Discrete & Continuous Dynamical Systems  B, 2013, 18 (6) : 16631681. doi: 10.3934/dcdsb.2013.18.1663 
[19] 
A. R. Humphries, O. A. DeMasi, F. M. G. Magpantay, F. Upham. Dynamics of a delay differential equation with multiple statedependent delays. Discrete & Continuous Dynamical Systems  A, 2012, 32 (8) : 27012727. doi: 10.3934/dcds.2012.32.2701 
[20] 
Loïs Boullu, Mostafa Adimy, Fabien Crauste, Laurent PujoMenjouet. Oscillations and asymptotic convergence for a delay differential equation modeling platelet production. Discrete & Continuous Dynamical Systems  B, 2019, 24 (6) : 24172442. doi: 10.3934/dcdsb.2018259 
2018 Impact Factor: 1.313
Tools
Metrics
Other articles
by authors
[Back to Top]