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On a delay differential equation arising from a car-following model: Wavefront solutions with constant-speed and their stability
University of Hamburg, Department of Mathematics, Bundesstrasse 55,20146 Hamburg, Germany |
$ z^{\prime\prime}(t)=h^2\,V(z(t-1)-z(t))+h\,z^\prime(t) $ |
$h$ |
$V$ |
$z(t)=c\,t+d$ |
$t∈\mathbb{R}$ |
$c,d∈\mathbb{R}$ |
$c\not=0$ |
$h$ |
References:
[1] |
M. Bando, K. Hasebe, A. Nakayama, A. Shibata and Y. Sugiyama,
Structure stability of congestion in traffic dynamics, Japan Journal of Industrial and Applied Mathematics, 11 (1994), 203-223.
doi: 10.1007/BF03167222. |
[2] |
M. Bando, K. Hasebe, A. Nakayama, A. Shibata and Y. Sugiyama,
Dynamical model of traffic congestion and numerical simulation, Physical Review E, 51 (1995), 1035-1042.
doi: 10.1103/PhysRevE.51.1035. |
[3] |
O. Diekmann, S. A. van Gils, S. M. Verduyn Lunel and H. -O. Walther,
Delay Equations. Functional, Complex, and Nonlinear Analysis, Applied Mathematical Sciences, 110, Springer-Verlag, New York, 1995.
doi: 10.1007/978-1-4612-4206-2. |
[4] |
I. Gasser and E. Stumpf, work in progress. Google Scholar |
[5] |
J. K. Hale and S. M. Verduyn Lunel,
Introduction to Functional Differential Equations, Applied Mathematical Sciences, 99, Springer-Verlag, New York, 1993.
doi: 10.1007/978-1-4612-4342-7. |
[6] |
T. Insperger and G. Stépán,
Semi-discretization for Time-Delay Systems. Stability and Engineering Applications, Applied Mathematical Sciences, 178, Springer-Verlag, New York, 2011.
doi: 10.1007/978-1-4614-0335-7. |
[7] |
MATLAB R2016a, The MathWorks Inc. , Natick, Massachusetts, 2016. Google Scholar |
[8] |
E. Stumpf, work in progress. Google Scholar |
show all references
References:
[1] |
M. Bando, K. Hasebe, A. Nakayama, A. Shibata and Y. Sugiyama,
Structure stability of congestion in traffic dynamics, Japan Journal of Industrial and Applied Mathematics, 11 (1994), 203-223.
doi: 10.1007/BF03167222. |
[2] |
M. Bando, K. Hasebe, A. Nakayama, A. Shibata and Y. Sugiyama,
Dynamical model of traffic congestion and numerical simulation, Physical Review E, 51 (1995), 1035-1042.
doi: 10.1103/PhysRevE.51.1035. |
[3] |
O. Diekmann, S. A. van Gils, S. M. Verduyn Lunel and H. -O. Walther,
Delay Equations. Functional, Complex, and Nonlinear Analysis, Applied Mathematical Sciences, 110, Springer-Verlag, New York, 1995.
doi: 10.1007/978-1-4612-4206-2. |
[4] |
I. Gasser and E. Stumpf, work in progress. Google Scholar |
[5] |
J. K. Hale and S. M. Verduyn Lunel,
Introduction to Functional Differential Equations, Applied Mathematical Sciences, 99, Springer-Verlag, New York, 1993.
doi: 10.1007/978-1-4612-4342-7. |
[6] |
T. Insperger and G. Stépán,
Semi-discretization for Time-Delay Systems. Stability and Engineering Applications, Applied Mathematical Sciences, 178, Springer-Verlag, New York, 2011.
doi: 10.1007/978-1-4614-0335-7. |
[7] |
MATLAB R2016a, The MathWorks Inc. , Natick, Massachusetts, 2016. Google Scholar |
[8] |
E. Stumpf, work in progress. Google Scholar |







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