- -

Chaotic asymptotic behaviour of the solutions of the Lighthill Whitham Richards equation

RiuNet: Institutional repository of the Polithecnic University of Valencia

Share/Send to

Cited by

Statistics

Chaotic asymptotic behaviour of the solutions of the Lighthill Whitham Richards equation

Show full item record

Conejero, JA.; Martínez Jiménez, F.; Peris Manguillot, A.; Ródenas Escribá, FDA. (2016). Chaotic asymptotic behaviour of the solutions of the Lighthill Whitham Richards equation. Nonlinear Dynamics. 84(1):127-133. doi:10.1007/s11071-015-2245-4

Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/99754

Files in this item

Item Metadata

Title: Chaotic asymptotic behaviour of the solutions of the Lighthill Whitham Richards equation
Author:
UPV Unit: Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada
Issued date:
Abstract:
[EN] The phenomenon of chaos has been exhibited in mathematical nonlinear models that describe traffic flows, see, for instance (Li and Gao in Modern Phys Lett B 18(26-27):1395-1402, 2004; Li in Phys. D Nonlinear Phenom ...[+]
Subjects: Devaney chaos , Mixing measures , Traffic , Lighthill Whitman Richards equation , C_0 -semigroup
Copyrigths: Reserva de todos los derechos
Source:
Nonlinear Dynamics. (issn: 0924-090X )
DOI: 10.1007/s11071-015-2245-4
Publisher:
Springer-Verlag
Publisher version: http://doi.org/10.1007/s11071-015-2245-4
Thanks:
The authors are supported by MEC Project MTM2013-47093-P. The second and third authors are supported by GVA, Project PROMETEOII/2013/013
Type: Artículo

References

Albanese, A.A., Barrachina, X., Mangino, E.M., Peris, A.: Distributional chaos for strongly continuous semigroups of operators. Commun. Pure Appl. Anal. 12(5), 2069–2082 (2013)

Aroza, J., Peris, A.: Chaotic behaviour of birth-and-death models with proliferation. J. Differ. Equ. Appl. 18(4), 647–655 (2012)

Banasiak, J., Lachowicz, M.: Chaos for a class of linear kinetic models. C. R. Acad. Sci. Paris Sér. II 329, 439–444 (2001) [+]
Albanese, A.A., Barrachina, X., Mangino, E.M., Peris, A.: Distributional chaos for strongly continuous semigroups of operators. Commun. Pure Appl. Anal. 12(5), 2069–2082 (2013)

Aroza, J., Peris, A.: Chaotic behaviour of birth-and-death models with proliferation. J. Differ. Equ. Appl. 18(4), 647–655 (2012)

Banasiak, J., Lachowicz, M.: Chaos for a class of linear kinetic models. C. R. Acad. Sci. Paris Sér. II 329, 439–444 (2001)

Banasiak, J., Lachowicz, M.: Topological chaos for birth-and-death-type models with proliferation. Math. Models Methods Appl. Sci. 12(6), 755–775 (2002)

Banasiak, J., Moszyński, M.: A generalization of Desch–Schappacher–Webb criteria for chaos. Discrete Contin. Dyn. Syst. 12(5), 959–972 (2005)

Banasiak, J., Moszyński, M.: Dynamics of birth-and-death processes with proliferation—stability and chaos. Discrete Contin. Dyn. Syst. 29(1), 67–79 (2011)

Barrachina, X., Conejero, J.A.: Devaney chaos and distributional chaos in the solution of certain partial differential equations. Abstr. Appl. Anal. Art. ID 457019, 11 (2012)

Barrachina, X., Conejero, J.A., Murillo-Arcila, M., Seoane-Sepúlveda, J.B.: Distributional chaos for the forward and backward control traffic model (2015, preprint)

Bayart, F., Matheron, É.: Dynamics of Linear Operators, Cambridge Tracts in Mathematics, vol. 179. Cambridge University Press, Cambridge (2009)

Bayart, F., Matheron, É.: Mixing operators and small subsets of the circle. J Reine Angew. Math. (2015, to appear)

Bermúdez, T., Bonilla, A., Conejero, J.A., Peris, A.: Hypercyclic, topologically mixing and chaotic semigroups on Banach spaces. Stud. Math. 170(1), 57–75 (2005)

Bermúdez, T., Bonilla, A., Martínez-Giménez, F., Peris, A.: Li-Yorke and distributionally chaotic operators. J. Math. Anal. Appl. 373(1), 83–93 (2011)

Bernardes Jr, N.C., Bonilla, A., Müller, V., Peris, A.: Distributional chaos for linear operators. J. Funct. Anal. 265(9), 2143–2163 (2013)

Brackstone, M., McDonald, M.: Car-following: a historical review. Transp. Res. Part F Traffic Psychol. Behav. 2(4), 181–196 (1999)

Conejero, J.A., Lizama, C., Rodenas, F.: Chaotic behaviour of the solutions of the Moore–Gibson–Thompson equation. Appl. Math. Inf. Sci. 9(5), 1–6 (2015)

Conejero, J.A., Mangino, E.M.: Hypercyclic semigroups generated by Ornstein-Uhlenbeck operators. Mediterr. J. Math. 7(1), 101–109 (2010)

Conejero, J.A., Müller, V., Peris, A.: Hypercyclic behaviour of operators in a hypercyclic $$C_0$$ C 0 -semigroup. J. Funct. Anal. 244, 342–348 (2007)

Conejero, J.A., Murillo-Arcila, M., Seoane-Sepúlveda, J.B.: Linear chaos for the quick-thinking-driver model. Semigroup Forum (2015). doi: 10.1007/s00233-015-9704-6

Conejero, J.A., Peris, A., Trujillo, M.: Chaotic asymptotic behavior of the hyperbolic heat transfer equation solutions. Int. J. Bifur. Chaos Appl. Sci. Eng. 20(9), 2943–2947 (2010)

Conejero, J.A., Rodenas, F., Trujillo, M.: Chaos for the hyperbolic bioheat equation. Discrete Contin. Dyn. Syst. 35(2), 653–668 (2015)

Desch, W., Schappacher, W., Webb, G.F.: Hypercyclic and chaotic semigroups of linear operators. Ergod. Theory Dyn. Syst. 17(4), 793–819 (1997)

Engel, K.-J., Nagel, R.: One-parameter semigroups for linear evolution equations, Graduate Texts in Mathematics, vol. 194. Springer, New York (2000). With contributions by S. Brendle, M. Campiti, T. Hahn, G. Metafune, G. Nickel, D. Pallara, C. Perazzoli, A. Rhandi, S. Romanelli and R. Schnaubelt

Grosse-Erdmann, K.-G., Peris Manguillot, A.: Linear Chaos. Universitext. Springer, London (2011)

Herzog, G.: On a universality of the heat equation. Math. Nachr. 188, 169–171 (1997)

Li, K., Gao, Z.: Nonlinear dynamics analysis of traffic time series. Modern Phys. Lett. B 18(26–27), 1395–1402 (2004)

Li, T.: Nonlinear dynamics of traffic jams. Phys. D Nonlinear Phenom. 207(1–2), 41–51 (2005)

Lustri, C.: Continuum Modelling of Traffic Flow. Special Topic Report. Oxford University, Oxford (2010)

Lighthill, M.J., Whitham, G.B.: On kinematic waves. II. A theory of traffic flow on long crowded roads. Proc. R. Soc. Lond. Ser. A. 229, 317–345 (1955)

Maerivoet, S., De Moor, B.: Cellular automata models of road traffic. Phys. Rep. 419(1), 1–64 (2005)

Mangino, E.M., Peris, A.: Frequently hypercyclic semigroups. Stud. Math. 202(3), 227–242 (2011)

Murillo-Arcila, M., Peris, A.: Strong mixing measures for linear operators and frequent hypercyclicity. J. Math. Anal. Appl. 398, 462–465 (2013)

Murillo-Arcila, M., Peris, A.: Strong mixing measures for $$C_0$$ C 0 -semigroups. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Math. RACSAM 109(1), 101–115 (2015)

Pazy, A.: Semigroups of Linear Operators and Applications to Partial Differential Equations, Applied Mathematical Sciences, vol. 44. Springer, New York (1983)

Protopopescu, V., Azmy, Y.Y.: Topological chaos for a class of linear models. Math. Models Methods Appl. Sci. 2(1), 79–90 (1992)

Richards, P.I.: Shock waves on the highway. Oper. Res. 4, 42–51 (1956)

[-]

This item appears in the following Collection(s)

Show full item record