Using MatContM in the study of a nonlinear map in economics

Niels Neirynck, Bashir Al-Hdaibat, Willy Govaerts, Iouri Aleksandrovitsj Kouznetsov, Hil Gaétan Ellart Meijer

    Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

    5 Citations (Scopus)
    47 Downloads (Pure)

    Abstract

    MatContM is a MATLAB interactive toolbox for the numerical study of iterated smooth maps, their Lyapunov exponents, fixed points, and periodic, homoclinic and heteroclinic orbits as well as their stable and unstable invariant manifolds. The bifurcation analysis is based on continuation methods, tracing out solution manifolds of various types of objects while some of the parameters of the map vary. In particular, MatContM computes codimension 1 bifurcation curves of cycles and supports the computation of the normal form coefficients of their codimension two bifurcations, and allows branch switching from codimension 2 points to secondary curves. MatContM builds on an earlier command-line MATLAB package CL MatContM but provides new computational routines and functionalities, as well as a graphical user interface, enabling interactive control of all computations, data handling and archiving. We apply MatContM in our study of the monopoly model of T. Puu with cubic price and quadratic marginal cost functions. Using MatContM, we analyze the fixed points and their stability and we compute branches of solutions of period 5, 10, 13 17. The chaotic and periodic behavior of the monopoly model is further analyzed by computing the largest Lyapunov exponents.
    Original languageUndefined
    Title of host publicationInternational Workshop on Nonlinear Maps and Applications, NOMA '15
    Place of PublicationBristol
    PublisherIOP
    Pages012013
    Number of pages6
    DOIs
    Publication statusPublished - Feb 2016

    Publication series

    NameJournal of Physics: Conference Series
    PublisherIOP
    Numberconference 1
    Volume692
    ISSN (Print)1742-6588
    ISSN (Electronic)1742-6596

    Keywords

    • EWI-27102
    • IR-102415
    • METIS-319435

    Cite this

    Neirynck, N., Al-Hdaibat, B., Govaerts, W., Kouznetsov, I. A., & Meijer, H. G. E. (2016). Using MatContM in the study of a nonlinear map in economics. In International Workshop on Nonlinear Maps and Applications, NOMA '15 (pp. 012013). (Journal of Physics: Conference Series; Vol. 692, No. conference 1). Bristol: IOP. https://doi.org/10.1088/1742-6596/692/1/012013
    Neirynck, Niels ; Al-Hdaibat, Bashir ; Govaerts, Willy ; Kouznetsov, Iouri Aleksandrovitsj ; Meijer, Hil Gaétan Ellart. / Using MatContM in the study of a nonlinear map in economics. International Workshop on Nonlinear Maps and Applications, NOMA '15. Bristol : IOP, 2016. pp. 012013 (Journal of Physics: Conference Series; conference 1).
    @inproceedings{80244ab63fce496b834335e42abe9389,
    title = "Using MatContM in the study of a nonlinear map in economics",
    abstract = "MatContM is a MATLAB interactive toolbox for the numerical study of iterated smooth maps, their Lyapunov exponents, fixed points, and periodic, homoclinic and heteroclinic orbits as well as their stable and unstable invariant manifolds. The bifurcation analysis is based on continuation methods, tracing out solution manifolds of various types of objects while some of the parameters of the map vary. In particular, MatContM computes codimension 1 bifurcation curves of cycles and supports the computation of the normal form coefficients of their codimension two bifurcations, and allows branch switching from codimension 2 points to secondary curves. MatContM builds on an earlier command-line MATLAB package CL MatContM but provides new computational routines and functionalities, as well as a graphical user interface, enabling interactive control of all computations, data handling and archiving. We apply MatContM in our study of the monopoly model of T. Puu with cubic price and quadratic marginal cost functions. Using MatContM, we analyze the fixed points and their stability and we compute branches of solutions of period 5, 10, 13 17. The chaotic and periodic behavior of the monopoly model is further analyzed by computing the largest Lyapunov exponents.",
    keywords = "EWI-27102, IR-102415, METIS-319435",
    author = "Niels Neirynck and Bashir Al-Hdaibat and Willy Govaerts and Kouznetsov, {Iouri Aleksandrovitsj} and Meijer, {Hil Ga{\'e}tan Ellart}",
    note = "10.1088/1742-6596/692/1/012013",
    year = "2016",
    month = "2",
    doi = "10.1088/1742-6596/692/1/012013",
    language = "Undefined",
    series = "Journal of Physics: Conference Series",
    publisher = "IOP",
    number = "conference 1",
    pages = "012013",
    booktitle = "International Workshop on Nonlinear Maps and Applications, NOMA '15",

    }

    Neirynck, N, Al-Hdaibat, B, Govaerts, W, Kouznetsov, IA & Meijer, HGE 2016, Using MatContM in the study of a nonlinear map in economics. in International Workshop on Nonlinear Maps and Applications, NOMA '15. Journal of Physics: Conference Series, no. conference 1, vol. 692, IOP, Bristol, pp. 012013. https://doi.org/10.1088/1742-6596/692/1/012013

    Using MatContM in the study of a nonlinear map in economics. / Neirynck, Niels; Al-Hdaibat, Bashir; Govaerts, Willy; Kouznetsov, Iouri Aleksandrovitsj; Meijer, Hil Gaétan Ellart.

    International Workshop on Nonlinear Maps and Applications, NOMA '15. Bristol : IOP, 2016. p. 012013 (Journal of Physics: Conference Series; Vol. 692, No. conference 1).

    Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

    TY - GEN

    T1 - Using MatContM in the study of a nonlinear map in economics

    AU - Neirynck, Niels

    AU - Al-Hdaibat, Bashir

    AU - Govaerts, Willy

    AU - Kouznetsov, Iouri Aleksandrovitsj

    AU - Meijer, Hil Gaétan Ellart

    N1 - 10.1088/1742-6596/692/1/012013

    PY - 2016/2

    Y1 - 2016/2

    N2 - MatContM is a MATLAB interactive toolbox for the numerical study of iterated smooth maps, their Lyapunov exponents, fixed points, and periodic, homoclinic and heteroclinic orbits as well as their stable and unstable invariant manifolds. The bifurcation analysis is based on continuation methods, tracing out solution manifolds of various types of objects while some of the parameters of the map vary. In particular, MatContM computes codimension 1 bifurcation curves of cycles and supports the computation of the normal form coefficients of their codimension two bifurcations, and allows branch switching from codimension 2 points to secondary curves. MatContM builds on an earlier command-line MATLAB package CL MatContM but provides new computational routines and functionalities, as well as a graphical user interface, enabling interactive control of all computations, data handling and archiving. We apply MatContM in our study of the monopoly model of T. Puu with cubic price and quadratic marginal cost functions. Using MatContM, we analyze the fixed points and their stability and we compute branches of solutions of period 5, 10, 13 17. The chaotic and periodic behavior of the monopoly model is further analyzed by computing the largest Lyapunov exponents.

    AB - MatContM is a MATLAB interactive toolbox for the numerical study of iterated smooth maps, their Lyapunov exponents, fixed points, and periodic, homoclinic and heteroclinic orbits as well as their stable and unstable invariant manifolds. The bifurcation analysis is based on continuation methods, tracing out solution manifolds of various types of objects while some of the parameters of the map vary. In particular, MatContM computes codimension 1 bifurcation curves of cycles and supports the computation of the normal form coefficients of their codimension two bifurcations, and allows branch switching from codimension 2 points to secondary curves. MatContM builds on an earlier command-line MATLAB package CL MatContM but provides new computational routines and functionalities, as well as a graphical user interface, enabling interactive control of all computations, data handling and archiving. We apply MatContM in our study of the monopoly model of T. Puu with cubic price and quadratic marginal cost functions. Using MatContM, we analyze the fixed points and their stability and we compute branches of solutions of period 5, 10, 13 17. The chaotic and periodic behavior of the monopoly model is further analyzed by computing the largest Lyapunov exponents.

    KW - EWI-27102

    KW - IR-102415

    KW - METIS-319435

    U2 - 10.1088/1742-6596/692/1/012013

    DO - 10.1088/1742-6596/692/1/012013

    M3 - Conference contribution

    T3 - Journal of Physics: Conference Series

    SP - 012013

    BT - International Workshop on Nonlinear Maps and Applications, NOMA '15

    PB - IOP

    CY - Bristol

    ER -

    Neirynck N, Al-Hdaibat B, Govaerts W, Kouznetsov IA, Meijer HGE. Using MatContM in the study of a nonlinear map in economics. In International Workshop on Nonlinear Maps and Applications, NOMA '15. Bristol: IOP. 2016. p. 012013. (Journal of Physics: Conference Series; conference 1). https://doi.org/10.1088/1742-6596/692/1/012013