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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 180595, 13 pages
Analytic Solutions for a Functional Differential Equation Related to a Traffic Flow Model
School of Mathematics, Chongqing Normal University, Chongqing 401331, China
Received 19 July 2012; Accepted 23 October 2012
Academic Editor: Antonio Suárez
Copyright © 2012 Houyu Zhao. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- I. Gasser, G. Sirito, and B. Werner, “Bifurcation analysis of a class of `car following' traffic models,” Physica D, vol. 197, no. 3-4, pp. 222–241, 2004.
- J. M. Greenberg, “Extensions and amplifications of a traffic model of Aw and Rascle,” SIAM Journal on Applied Mathematics, vol. 62, no. 3, pp. 729–745, 2001/02.
- J. M. Greenberg, “Congestion redux,” SIAM Journal on Applied Mathematics, vol. 64, no. 4, pp. 1175–1185, 2004.
- M. Herty and R. Illner, “On stop-and-go waves in dense traffic,” Kinetic and Related Models, vol. 1, no. 3, pp. 437–452, 2008.
- M. Herty and R. Illner, “Analytical and numerical investigations of refined macroscopic traffic flow models,” Kinetic and Related Models, vol. 3, no. 2, pp. 311–333, 2010.
- R. Illner and G. McGregor, “On a functional-differential equation arising from a traffic flow model,” SIAM Journal on Applied Mathematics, vol. 72, no. 2, pp. 623–645, 2012.
- R. Illner, A. Klar, and T. Materne, “Vlasov-Fokker-Planck models for multilane traffic flow,” Communications in Mathematical Sciences, vol. 1, no. 1, pp. 1–12, 2003.
- B. Kerner, The Physics of Traffic, Springer, Berlin, Germany, 2004.
- J. P. Lebacque, “Les modèles macroscopiques de trafic,” Annales des Ponts, no. 67, pp. 28–45, 1993.
- W. Knospe, L. Santen, A. Schadschneider, and M. Schreckenberg, “Towards a realistic microscopic description of highway traffic,” Journal of Physics A, vol. 33, no. 48, pp. L477–L485, 2000.
- A. Sopasakis and M. A. Katsoulakis, “Stochastic modeling and simulation of traffic flow: asymmetric single exclusion process with Arrhenius look-ahead dynamics,” SIAM Journal on Applied Mathematics, vol. 66, no. 3, pp. 921–944, 2006.
- M. Treiber and D. Helbing, “Macroscopic simulation of widely scattered synchronized traffic states,” Journal of Physics A, vol. 32, no. 1, pp. L17–L23, 1999.
- H. M. Zhang, “A non-equilibrium traffic model devoid of gas-like behavior,” Transportation Research Part B, vol. 36, no. 3, pp. 275–290, 2002.
- A. Aw and M. Rascle, “Resurrection of ‘second order’ models of traffic flow,” SIAM Journal on Applied Mathematics, vol. 60, no. 3, pp. 916–938, 2000.
- T. Alperovich and A. Sopasakis, “Stochastic description of traffic flow,” Journal of Statistical Physics, vol. 133, no. 6, pp. 1083–1105, 2008.
- J. Si, W. Zhang, and G.-H. Kim, “Analytic solutions of an iterative functional differential equation,” Applied Mathematics and Computation, vol. 150, no. 3, pp. 647–659, 2004.
- J. Si and M. Ma, “Local invertible analytic solution of a functional differential equation with deviating arguments depending on the state derivative,” Journal of Mathematical Analysis and Applications, vol. 327, no. 1, pp. 723–734, 2007.
- A. D. Bjuno, “Analytic form of differential equations,” Transactions of the Moscow Mathematical Society, vol. 25, pp. 131–288, 1971.
- S. Marmi, P. Moussa, and J.-C. Yoccoz, “The Brjuno functions and their regularity properties,” Communications in Mathematical Physics, vol. 186, no. 2, pp. 265–293, 1997.
- T. Carletti and S. Marmi, “Linearization of analytic and non-analytic germs of diffeomorphisms of ,” Bulletin de la Société Mathématique de France, vol. 128, no. 1, pp. 69–85, 2000.
- A. M. Davie, “The critical function for the semistandard map,” Nonlinearity, vol. 7, no. 1, pp. 219–229, 1994.