DDE-BIFTOOL v. 3.1.1 Manual — Bifurcation analysis of delay differential equations
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J. Sieber | K. Engelborghs | D. Roose | T. Luzyanina | G. Samaey | D. Roose | G. Samaey | K. Engelborghs | T. Luzyanina | J. Sieber
[1] R. Bellman,et al. Differential-Difference Equations , 1967 .
[2] R. Seydel. Practical bifurcation and stability analysis : from equilibrium to chaos , 1994 .
[3] L. Shampine. Solving Delay Differential Equations with dde 23 , 2000 .
[4] Willy Govaerts,et al. MATCONT: A MATLAB package for numerical bifurcation analysis of ODEs , 2003, TOMS.
[5] D. Roose,et al. Continuation and Bifurcation Analysis of Delay Differential Equations , 2007 .
[6] John Mallet-Paret,et al. Stability of periodic solutions of state-dependent delay-differential equations , 2011 .
[7] Dirk Roose,et al. Numerical bifurcation analysis of delay differential equations using DDE-BIFTOOL , 2002, TOMS.
[8] Frank Schilder,et al. Recipes for Continuation , 2013, Computational science and engineering.
[9] Dirk Roose,et al. Numerical computation of stability and detection of Hopf bifurcations of steady state solutions of delay differential equations , 1999, Adv. Comput. Math..
[10] Sue Ann Campbell,et al. Stability, Bifurcation, and Multistability in a System of Two Coupled Neurons with Multiple Time Delays , 2000, SIAM J. Appl. Math..
[11] R. Vermiglio,et al. TRACE-DDE: a Tool for Robust Analysis and Characteristic Equations for Delay Differential Equations , 2009 .
[12] John L. Casti,et al. Introduction to the theory and application of differential equations with deviating arguments , 1973 .
[13] P. Holmes,et al. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.
[14] J. Hale,et al. Methods of Bifurcation Theory , 1996 .
[15] Pak Chiu Leung,et al. Numerical bifurcation analysis of delay differential equations , 1982 .
[16] Koen Engelborghs,et al. Stability of piecewise polynomial collocation for computing periodic solutions of delay differential equations , 2002, Numerische Mathematik.
[17] J. Hale. Theory of Functional Differential Equations , 1977 .
[18] John Argyris,et al. An Exploration of Chaos: An Introduction for Natural Scientists and Engineers , 1994 .
[19] Giovanni Samaey,et al. Numerical Computation of Connecting Orbits in Delay Differential Equations , 2002, Numerical Algorithms.
[20] V. Kolmanovskii,et al. Applied Theory of Functional Differential Equations , 1992 .
[21] Jan Sieber,et al. Finding periodic orbits in state-dependent delay differential equations as roots of algebraic equations , 2010, 1010.2391.
[22] Christopher A. H. Paul,et al. A User-Guide to Archi - An Explicit Runge-Kutta Code for Solving Delay and Neutral Differential Equa , 1995 .
[23] J. A. Kuznecov. Elements of applied bifurcation theory , 1998 .
[24] Jianhong Wu,et al. Introduction to Functional Differential Equations , 2013 .
[25] Ernst Hairer,et al. Stiff delay equations , 2007, Scholarpedia.
[26] D. Sarafyan,et al. DKLAG6: a code based on continuously imbedded sixth-order Runge-Kutta methods for the solution of state-dependent functional differential equations , 1997 .
[27] K. ENGELBORGHS,et al. On Stability of LMS Methods and Characteristic Roots of Delay Differential Equations , 2002, SIAM J. Numer. Anal..
[28] R. D. Driver,et al. Ordinary and Delay Differential Equations , 1977 .
[29] Dirk Roose,et al. Collocation Methods for the Computation of Periodic Solutions of Delay Differential Equations , 2000, SIAM J. Sci. Comput..
[30] B. I. Wage,et al. Normal form computations for Delay Differential Equations in DDE-BIFTOOL , 2014 .
[31] Eusebius J. Doedel,et al. Lecture Notes on Numerical Analysis of Nonlinear Equations , 2007 .
[32] Gábor Stépán,et al. Continuation of Bifurcations in Periodic Delay-Differential Equations Using Characteristic Matrices , 2006, SIAM J. Sci. Comput..
[33] Willy Govaerts,et al. Numerical methods for bifurcations of dynamical equilibria , 1987 .
[34] Dirk Roose,et al. Efficient computation of characteristic roots of delay differential equations using LMS methods , 2008 .
[35] R. Eddie Wilson,et al. Collocation schemes for periodic solutions of neutral delay differential equations , 2006 .
[36] Dirk Roose,et al. Numerical bifurcation Analysis of differential equations with State-Dependent Delay , 2001, Int. J. Bifurc. Chaos.
[37] J. Kato. Stability in functional differential equations , 1980 .
[38] Wayne H. Enright,et al. A delay differential equation solver based on a continuous Runge–Kutta method with defect control , 1997, Numerical Algorithms.
[39] Dirk Roose,et al. Numerical stability analysis and computation of Hopf bifurcation points for delay differential equations , 1996 .
[40] Tian Hong-jiong,et al. The numerical stability of linear multistep methods for delay differential equations with many delays , 1996 .