IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v161y2022ics0960077922005550.html
   My bibliography  Save this article

Parameterized stable/unstable manifolds for periodic solutions of implicitly defined dynamical systems

Author

Listed:
  • Timsina, Archana Neupane
  • Mireles James, J.D.

Abstract

We develop a multiple shooting parameterization method for studying stable/unstable manifolds attached to periodic orbits of systems whose dynamics is determined by an implicit rule. We represent the local invariant manifold using high order polynomials and show that the method leads to efficient numerical calculations. We implement the method for several example systems in dimension two and three. The resulting manifolds provide useful information about the orbit structure of the implicit system even in the case that the implicit relation is neither invertible nor single-valued.

Suggested Citation

  • Timsina, Archana Neupane & Mireles James, J.D., 2022. "Parameterized stable/unstable manifolds for periodic solutions of implicitly defined dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    • Handle: RePEc:eee:chsofr:v:161:y:2022:i:c:s0960077922005550
    DOI: 10.1016/j.chaos.2022.112345
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077922005550
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2022.112345?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Michener, Ronald & Ravikumar, B., 1998. "Chaotic dynamics in a cash-in-advance economy," Journal of Economic Dynamics and Control, Elsevier, vol. 22(7), pages 1117-1137, May.
    2. Kennedy, Judy A. & Stockman, David R., 2008. "Chaotic equilibria in models with backward dynamics," Journal of Economic Dynamics and Control, Elsevier, vol. 32(3), pages 939-955, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kennedy, Judy & Stockman, David R. & Yorke, James A., 2008. "The inverse limits approach to chaos," Journal of Mathematical Economics, Elsevier, vol. 44(5-6), pages 423-444, April.
    2. Airaudo, Marco, 2016. "Endogenous Stock Price Fluctuations with Dynamic Self-Control Preferences," School of Economics Working Paper Series 2016-2, LeBow College of Business, Drexel University.
    3. Gardini, Laura & Hommes, Cars & Tramontana, Fabio & de Vilder, Robin, 2009. "Forward and backward dynamics in implicitly defined overlapping generations models," Journal of Economic Behavior & Organization, Elsevier, vol. 71(2), pages 110-129, August.
    4. David R. Stockman, 2008. "Uniform Measures On Inverse Limit Spaces," Working Papers 08-25, University of Delaware, Department of Economics.
    5. David Stockman & Judy Kennedy & James Yorke, 2006. "Inverse Limits and Models with Backward Dynamics," Working Papers 06-12, University of Delaware, Department of Economics.
    6. David R. Stockman & Judy Kennedy & Brian Raines, 2007. "Expected Utility in Models with Chaos," Working Papers 07-16, University of Delaware, Department of Economics.
    7. Nika Lazaryan & Thomas A. Lubik, 2019. "Global dynamics in a search and matching model of the labor market," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 68(2), pages 461-497, September.
    8. Tim Hursey & Alexander L. Wolman, 2010. "Monetary policy and global equilibria in a production economy," Economic Quarterly, Federal Reserve Bank of Richmond, vol. 96(4Q), pages 317-337.
    9. Maxime Menuet & Alexandru Minea & Patrick Villieu, 2018. "Deficit, monetization, and economic growth: a case for multiplicity and indeterminacy," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 65(4), pages 819-853, June.
    10. Stockman, David R., 2010. "Balanced-budget rules: Chaos and deterministic sunspots," Journal of Economic Theory, Elsevier, vol. 145(3), pages 1060-1085, May.
    11. Chen, Hung-Ju & Li, Ming-Chia, 2008. "Chaotic dynamics in a monetary economy with habit persistence," Journal of Economic Behavior & Organization, Elsevier, vol. 65(2), pages 245-260, February.
    12. Grandmont, Jean-Michel, 2008. "Nonlinear difference equations, bifurcations and chaos: An introduction," Research in Economics, Elsevier, vol. 62(3), pages 122-177, September.
    13. Stockman, David R., 2009. "Chaos and sector-specific externalities," Journal of Economic Dynamics and Control, Elsevier, vol. 33(12), pages 2030-2046, December.
    14. Schabert, Andreas, 2010. "Monetary policy under a fiscal theory of sovereign default," Journal of Economic Theory, Elsevier, vol. 145(2), pages 860-868, March.
    15. Fukuda, Shin-ichi, 2004. "Extraneous shocks and international linkage of business cycles in a two-country monetary model," Journal of Economic Behavior & Organization, Elsevier, vol. 54(3), pages 389-409, July.
    16. David R. Stockman & Judy Kennedy & James A. Yorke, 2005. " Inverse Limits and Models with Ill-Defined Forward Dynamics," Working Papers 05-06, University of Delaware, Department of Economics.
    17. Jess Benhabib & Jianjun Miao & Pengfei Wang, 2016. "Chaotic banking crises and regulations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(2), pages 393-422, February.
    18. Joydeep Bhattacharya & Helle Bunzel, 2003. "Dynamics of the planning solution in the discrete-time textbook model of labor market search and matching," Economics Bulletin, AccessEcon, vol. 5(19), pages 1-10.
    19. Bosi, Stefano & Ismael, Mohanad & Venditti, Alain, 2016. "Collateral and growth cycles with heterogeneous agents," Journal of Macroeconomics, Elsevier, vol. 48(C), pages 327-350.
    20. Piazza, Roberto, 2016. "Self-fulfilling deflations," Journal of Economic Dynamics and Control, Elsevier, vol. 73(C), pages 18-40.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:161:y:2022:i:c:s0960077922005550. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.