- -

Nonlocal operators are chaotic

RiuNet: Repositorio Institucional de la Universidad Politécnica de Valencia

Compartir/Enviar a

Citas

Estadísticas

  • Estadisticas de Uso

Nonlocal operators are chaotic

Mostrar el registro sencillo del ítem

Ficheros en el ítem

Thumbnail
Nombre: Lzama;Murllo;Pers ...
Tamaño: 501.8Kb
Formato: PDF
Descripción: Versión del Autor.
Abrir
[Cerrado]
Nombre: 5.0018408.pdf
Tamaño: 455.7Kb
Formato: PDF
Descripción: Versión editorial
Solicitar una copia al autor
dc.contributor.author Lizama, Carlos es_ES
dc.contributor.author Murillo Arcila, Marina es_ES
dc.contributor.author Peris Manguillot, Alfredo es_ES
dc.date.accessioned 2021-05-14T03:32:12Z
dc.date.available 2021-05-14T03:32:12Z
dc.date.issued 2020-10 es_ES
dc.identifier.issn 1054-1500 es_ES
dc.identifier.uri http://hdl.handle.net/10251/166352
dc.description.abstract [EN] We characterize for the first time the chaotic behavior of nonlocal operators that come from a broad class of time-stepping schemes of approximation for fractional differential operators. For that purpose, we use criteria for chaos of Toeplitz operators in Lebesgue spaces of sequences. Surprisingly, this characterization is proved to be-in some cases-dependent of the fractional order of the operator and the step size of the scheme. es_ES
dc.description.sponsorship C. Lizama is partially supported by FONDECYT (Grant No. 1180041) and DICYT, Universidad de Santiago de Chile, USACH. M. Murillo-Arcila is supported by MICINN and FEDER, Projects MTM2016-75963-P and PID2019-105011GB-I00, and by Generalitat Valenciana, Project GVA/2018/110. A. Peris is supported by MICINN and FEDER, Projects MTM2016-75963-P and PID2019-105011GB-I00, and by Generalitat Valenciana, Project PROMETEO/2017/102. es_ES
dc.language Inglés es_ES
dc.publisher American Institute of Physics es_ES
dc.relation.ispartof Chaos An Interdisciplinary Journal of Nonlinear Science es_ES
dc.rights Reserva de todos los derechos es_ES
dc.subject Non-local operators es_ES
dc.subject Chaos es_ES
dc.subject Linear dynamics es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title Nonlocal operators are chaotic es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1063/5.0018408 es_ES
dc.relation.projectID info:eu-repo/grantAgreement/GVA//GV%2F2018%2F110/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/FONDECYT//1180041/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/MINECO//MTM2016-75963-P/ES/DINAMICA DE OPERADORES/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/GVA//PROMETEO%2F2017%2F102/ES/ANALISIS FUNCIONAL, TEORIA DE OPERADORES Y APLICACIONES/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-105011GB-I00/ES/DINAMICA DE OPERADORES/ es_ES
dc.rights.accessRights Abierto es_ES
dc.contributor.affiliation Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada es_ES
dc.description.bibliographicCitation Lizama, C.; Murillo Arcila, M.; Peris Manguillot, A. (2020). Nonlocal operators are chaotic. Chaos An Interdisciplinary Journal of Nonlinear Science. 30(10):1-8. https://doi.org/10.1063/5.0018408 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion https://doi.org/10.1063/5.0018408 es_ES
dc.description.upvformatpinicio 1 es_ES
dc.description.upvformatpfin 8 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 30 es_ES
dc.description.issue 10 es_ES
dc.relation.pasarela S\427222 es_ES
dc.contributor.funder Generalitat Valenciana es_ES
dc.contributor.funder Agencia Estatal de Investigación es_ES
dc.contributor.funder European Regional Development Fund es_ES
dc.contributor.funder Fondo Nacional de Desarrollo Científico y Tecnológico, Chile es_ES
dc.contributor.funder Departamento de Investigaciones Científicas y Tecnológicas, Universidad de Santiago de Chile es_ES
dc.contributor.funder Ministerio de Economía y Competitividad es_ES
dc.description.references Abadias, L., & Miana, P. J. (2018). Generalized Cesàro operators, fractional finite differences and Gamma functions. Journal of Functional Analysis, 274(5), 1424-1465. doi:10.1016/j.jfa.2017.10.010 es_ES
dc.description.references Atici, F. M., & Eloe, P. (2009). Discrete fractional calculus with the nabla operator. Electronic Journal of Qualitative Theory of Differential Equations, (3), 1-12. doi:10.14232/ejqtde.2009.4.3 es_ES
dc.description.references Atıcı, F. M., & Eloe, P. W. (2011). Two-point boundary value problems for finite fractional difference equations. Journal of Difference Equations and Applications, 17(4), 445-456. doi:10.1080/10236190903029241 es_ES
dc.description.references Atici, F. M., & Eloe, P. W. (2008). Initial value problems in discrete fractional calculus. Proceedings of the American Mathematical Society, 137(03), 981-989. doi:10.1090/s0002-9939-08-09626-3 es_ES
dc.description.references Atıcı, F. M., & Şengül, S. (2010). Modeling with fractional difference equations. Journal of Mathematical Analysis and Applications, 369(1), 1-9. doi:10.1016/j.jmaa.2010.02.009 es_ES
dc.description.references Banks, J., Brooks, J., Cairns, G., Davis, G., & Stacey, P. (1992). On Devaney’s Definition of Chaos. The American Mathematical Monthly, 99(4), 332-334. doi:10.1080/00029890.1992.11995856 es_ES
dc.description.references Baranov, A., & Lishanskii, A. (2016). Hypercyclic Toeplitz Operators. Results in Mathematics, 70(3-4), 337-347. doi:10.1007/s00025-016-0527-x es_ES
dc.description.references Bayart, F., & Matheron, E. (2009). Dynamics of Linear Operators. doi:10.1017/cbo9780511581113 es_ES
dc.description.references DELAUBENFELS, R., & EMAMIRAD, H. (2001). Chaos for functions of discrete and continuous weighted shift operators. Ergodic Theory and Dynamical Systems, 21(05). doi:10.1017/s0143385701001675 es_ES
dc.description.references Edelman, M. (2014). Caputo standard α-family of maps: Fractional difference vs. fractional. Chaos: An Interdisciplinary Journal of Nonlinear Science, 24(2), 023137. doi:10.1063/1.4885536 es_ES
dc.description.references Edelman, M. (2015). On the fractional Eulerian numbers and equivalence of maps with long term power-law memory (integral Volterra equations of the second kind) to Grünvald-Letnikov fractional difference (differential) equations. Chaos: An Interdisciplinary Journal of Nonlinear Science, 25(7), 073103. doi:10.1063/1.4922834 es_ES
dc.description.references Edelman, M. (2015). Fractional Maps and Fractional Attractors. Part II: Fractional Difference Caputo α- Families of Maps. The interdisciplinary journal of Discontinuity, Nonlinearity, and Complexity, 4(4), 391-402. doi:10.5890/dnc.2015.11.003 es_ES
dc.description.references Erbe, L., Goodrich, C. S., Jia, B., & Peterson, A. (2016). Survey of the qualitative properties of fractional difference operators: monotonicity, convexity, and asymptotic behavior of solutions. Advances in Difference Equations, 2016(1). doi:10.1186/s13662-016-0760-3 es_ES
dc.description.references Ferreira, R. A. C. (2012). A discrete fractional Gronwall inequality. Proceedings of the American Mathematical Society, 140(5), 1605-1612. doi:10.1090/s0002-9939-2012-11533-3 es_ES
dc.description.references Ferreira, R. A. C. (2013). Existence and uniqueness of solution to some discrete fractional boundary value problems of order less than one. Journal of Difference Equations and Applications, 19(5), 712-718. doi:10.1080/10236198.2012.682577 es_ES
dc.description.references Goodrich, C., & Peterson, A. C. (2015). Discrete Fractional Calculus. doi:10.1007/978-3-319-25562-0 es_ES
dc.description.references Goodrich, C. S. (2012). On discrete sequential fractional boundary value problems. Journal of Mathematical Analysis and Applications, 385(1), 111-124. doi:10.1016/j.jmaa.2011.06.022 es_ES
dc.description.references Goodrich, C. S. (2014). A convexity result for fractional differences. Applied Mathematics Letters, 35, 58-62. doi:10.1016/j.aml.2014.04.013 es_ES
dc.description.references Goodrich, C., & Lizama, C. (2020). A transference principle for nonlocal operators using a convolutional approach: fractional monotonicity and convexity. Israel Journal of Mathematics, 236(2), 533-589. doi:10.1007/s11856-020-1991-2 es_ES
dc.description.references Gray, H. L., & Zhang, N. F. (1988). On a new definition of the fractional difference. Mathematics of Computation, 50(182), 513-529. doi:10.1090/s0025-5718-1988-0929549-2 es_ES
dc.description.references Li, K., Peng, J., & Jia, J. (2012). Cauchy problems for fractional differential equations with Riemann–Liouville fractional derivatives. Journal of Functional Analysis, 263(2), 476-510. doi:10.1016/j.jfa.2012.04.011 es_ES
dc.description.references Lizama, C. (2017). The Poisson distribution, abstract fractional difference equations, and stability. Proceedings of the American Mathematical Society, 145(9), 3809-3827. doi:10.1090/proc/12895 es_ES
dc.description.references Lizama, C. (2015). lp-maximal regularity for fractional difference equations on UMD spaces. Mathematische Nachrichten, 288(17-18), 2079-2092. doi:10.1002/mana.201400326 es_ES
dc.description.references Lizama, C., & Murillo-Arcila, M. (2020). Discrete maximal regularity for volterra equations and nonlocal time-stepping schemes. Discrete & Continuous Dynamical Systems - A, 40(1), 509-528. doi:10.3934/dcds.2020020 es_ES
dc.description.references Martínez-Giménez, F. (2007). Chaos for power series of backward shift operators. Proceedings of the American Mathematical Society, 135(6), 1741-1752. doi:10.1090/s0002-9939-07-08658-3 es_ES
dc.description.references Radwan, A. G., AbdElHaleem, S. H., & Abd-El-Hafiz, S. K. (2016). Symmetric encryption algorithms using chaotic and non-chaotic generators: A review. Journal of Advanced Research, 7(2), 193-208. doi:10.1016/j.jare.2015.07.002 es_ES
dc.description.references Radwan, A. G., Moaddy, K., Salama, K. N., Momani, S., & Hashim, I. (2014). Control and switching synchronization of fractional order chaotic systems using active control technique. Journal of Advanced Research, 5(1), 125-132. doi:10.1016/j.jare.2013.01.003 es_ES
dc.description.references Wu, G.-C., & Baleanu, D. (2013). Discrete fractional logistic map and its chaos. Nonlinear Dynamics, 75(1-2), 283-287. doi:10.1007/s11071-013-1065-7 es_ES
dc.description.references Wu, G.-C., Baleanu, D., & Zeng, S.-D. (2014). Discrete chaos in fractional sine and standard maps. Physics Letters A, 378(5-6), 484-487. doi:10.1016/j.physleta.2013.12.010 es_ES


Este ítem aparece en la(s) siguiente(s) colección(ones)

Mostrar el registro sencillo del ítem