IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v81y2010i1p52-61.html
   My bibliography  Save this article

Border collision bifurcations of superstable cycles in a one-dimensional piecewise smooth map

Author

Listed:
  • Brianzoni, Serena
  • Michetti, Elisabetta
  • Sushko, Iryna

Abstract

We study the dynamics of a one-dimensional piecewise smooth map defined by constant and logistic functions. This map has qualitatively the same dynamics as the one defined by constant and unimodal functions, coming from an economic application. Namely, it contributes to the investigation of a model of the evolution of corruption in public procurement proposed by Brianzoni et al. [4]. Bifurcation structure of the economically meaningful part of the parameter space is described, in particular, the fold and flip border-collision bifurcation curves of the superstable cycles are obtained. We show also how these bifurcations are related to the well-known saddle-node and period-doubling bifurcations.

Suggested Citation

  • Brianzoni, Serena & Michetti, Elisabetta & Sushko, Iryna, 2010. "Border collision bifurcations of superstable cycles in a one-dimensional piecewise smooth map," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(1), pages 52-61.
    • Handle: RePEc:eee:matcom:v:81:y:2010:i:1:p:52-61
    DOI: 10.1016/j.matcom.2010.06.018
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475410002193
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2010.06.018?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. Bajari, Patrick & Tadelis, Steven, 2001. "Incentives versus Transaction Costs: A Theory of Procurement Contracts," RAND Journal of Economics, The RAND Corporation, vol. 32(3), pages 387-407, Autumn.
    2. Celentani, Marco & Ganuza, Juan-Jose, 2002. "Corruption and competition in procurement," European Economic Review, Elsevier, vol. 46(7), pages 1273-1303, July.
    3. Bose, Niloy & Capasso, Salvatore & Murshid, Antu Panini, 2008. "Threshold Effects of Corruption: Theory and Evidence," World Development, Elsevier, vol. 36(7), pages 1173-1191, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Radi, Davide & Gardini, Laura & Avrutin, Viktor, 2014. "The role of constraints in a segregation model: The symmetric case," Chaos, Solitons & Fractals, Elsevier, vol. 66(C), pages 103-119.
    2. Anna Agliari & Pasquale Commendatore & Ilaria Foroni & Ingrid Kubin, 2011. "Border Collision Bifurcations in a Footloose Capital Model with First Nature Firms," Computational Economics, Springer;Society for Computational Economics, vol. 38(3), pages 349-366, October.
    3. Roya Makrooni & Laura Gardini, 2015. "Bifurcation structures in a family of one-dimensional linear-power discontinuous maps," Gecomplexity Discussion Paper Series 7, Action IS1104 "The EU in the new complex geography of economic systems: models, tools and policy evaluation", revised Jan 2015.
    4. Agliari, Anna & Commendatore, Pasquale & Foroni, Ilaria & Kubin, Ingrid, 2015. "Agglomeration dynamics and first nature asymmetries," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 108(C), pages 81-98.
    5. Sushko, Iryna & Gardini, Laura & Matsuyama, Kiminori, 2014. "Superstable credit cycles and U-sequence," Chaos, Solitons & Fractals, Elsevier, vol. 59(C), pages 13-27.
    6. Jose S. Cánovas & Anastasiia Panchuk & Tonu Puu, 2015. "Role of reinvestment in a competitive market," Gecomplexity Discussion Paper Series 12, Action IS1104 "The EU in the new complex geography of economic systems: models, tools and policy evaluation", revised Apr 2015.
    7. Brianzoni, Serena & Coppier, Raffaella & Michetti, Elisabetta, 2019. "Evolutionary effects of non-compliant behavior in public procurement," Structural Change and Economic Dynamics, Elsevier, vol. 51(C), pages 106-118.
    8. Brianzoni, Serena & Mammana, Cristiana & Michetti, Elisabetta, 2012. "Variable elasticity of substituition in a discrete time Solow–Swan growth model with differential saving," Chaos, Solitons & Fractals, Elsevier, vol. 45(1), pages 98-108.
    9. Radi, Davide & Gardini, Laura, 2015. "Entry limitations and heterogeneous tolerances in a Schelling-like segregation model," Chaos, Solitons & Fractals, Elsevier, vol. 79(C), pages 130-144.
    10. Cánovas, Jose S. & Panchuk, Anastasiia & Puu, Tönu, 2015. "Asymptotic dynamics of a piecewise smooth map modelling a competitive market," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 117(C), pages 20-38.
    11. Matsuo, Akihito & Asahara, Hiroyuki & Kousaka, Takuji, 2012. "Bifurcation structure of chaotic attractor in switched dynamical systems with spike noise," Chaos, Solitons & Fractals, Elsevier, vol. 45(6), pages 795-804.

    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. Serena Brianzoni & Raffaella Coppier & Elisabetta Michetti, 2015. "Multiple equilibria in a discrete time growth model with corruption in public procurement," Quality & Quantity: International Journal of Methodology, Springer, vol. 49(6), pages 2387-2410, November.
    2. Serena Brianzoni & Raffaella Coppier & Elisabetta Michetti, 2012. "A Growth Model with Corruption in Public Procurement: Equilibria and Policy Implications," Working Papers 68-2012, Macerata University, Department of Finance and Economic Sciences, revised Sep 2015.
    3. Peerayuth Charoensukmongkol & Murad Moqbel, 2014. "Does Investment in ICT Curb or Create More Corruption? A Cross-Country Analysis," Public Organization Review, Springer, vol. 14(1), pages 51-63, March.
    4. Leandro Arozamena & Federico Weinschelbaum & Juan-José Ganuza, 2021. "Renegotiation and Discrimination in Symmetric Procurement Auctions," Department of Economics Working Papers 2021_09, Universidad Torcuato Di Tella.
    5. Chiappinelli, Olga, 2020. "Political corruption in the execution of public contracts," Journal of Economic Behavior & Organization, Elsevier, vol. 179(C), pages 116-140.
    6. Brianzoni, Serena & Coppier, Raffaella & Michetti, Elisabetta, 2019. "Evolutionary effects of non-compliant behavior in public procurement," Structural Change and Economic Dynamics, Elsevier, vol. 51(C), pages 106-118.
    7. Tchablemane YENLIDE & Mawussé Komlagan Nézan OKEY, 2022. "Corruption et accès à l’électricité dans les pays de l’Afrique subsaharienne," Region et Developpement, Region et Developpement, LEAD, Universite du Sud - Toulon Var, vol. 55, pages 23-37.
    8. Pablo Ballesteros-P�rez & Martin Skitmore & Eugenio Pellicer & M. Carmen Gonz�lez-Cruz, 2015. "Scoring rules and abnormally low bids criteria in construction tenders: a taxonomic review," Construction Management and Economics, Taylor & Francis Journals, vol. 33(4), pages 259-278, April.
    9. Rodrigo Carril, 2021. "Rules Versus Discretion in Public Procurement," Working Papers 1232, Barcelona School of Economics.
    10. Massimo Finocchiaro Castro & Calogero Guccio & Giacomo Pignataro & Ilde Rizzo, 2018. "Is competition able to counteract the inefficiency of corruption? The case of Italian public works," Economia e Politica Industriale: Journal of Industrial and Business Economics, Springer;Associazione Amici di Economia e Politica Industriale, vol. 45(1), pages 55-84, March.
    11. Raffaella Coppier & Francesca Grassetti & Elisabetta Michetti, 2021. "Non-compliant behaviour in public procurement: an evolutionary model with endogenous monitoring," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(1), pages 459-483, June.
    12. Nicola Doni, 2007. "A Comparison of Alternative Procedures for the Selection of the Private Partner in PPP Projects," Working Papers - Economics wp2007_10, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.
    13. Francesco Decarolis & Raymond Fisman & Paolo Pinotti & Silvia Vannutelli, 2019. "Rules, Discretion, and Corruption in Procurement: Evidence from Italian Government Contracting," Boston University - Department of Economics - The Institute for Economic Development Working Papers Series dp-344, Boston University - Department of Economics.
    14. David Martimort & Flavio Menezes & Myrna Wooders & ELISABETTA IOSSA & DAVID MARTIMORT, 2015. "The Simple Microeconomics of Public-Private Partnerships," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 17(1), pages 4-48, February.
    15. Gil, Ricard & Marion, Justin, 2009. "The Role of Repeated Interactions, Self-Enforcing Agreements and Relational [Sub]Contracting: Evidence from California Highway Procurement Auctions," University of California Transportation Center, Working Papers qt7r14d10x, University of California Transportation Center.
    16. Elisabetta Iossa & David Martimort, 2012. "Risk allocation and the costs and benefits of public--private partnerships," RAND Journal of Economics, RAND Corporation, vol. 43(3), pages 442-474, September.
    17. François MARECHAL, 2003. "Should we base procurement rules on the competition of linear incentive contracts ?," Cahiers de Recherches Economiques du Département d'économie 03.07, Université de Lausanne, Faculté des HEC, Département d’économie.
    18. Barbosa, Klenio, 2009. "Free Riding in Procurement Design," TSE Working Papers 09-128, Toulouse School of Economics (TSE).
    19. repec:lic:licosd:18407 is not listed on IDEAS
    20. Luc Baumstark & Claude Ménard & William Roy & Anne Yvrande-Billon, 2005. "Modes de gestion et efficience des opérateurs dans le secteur des transports urbains de personnes," Post-Print halshs-00103116, HAL.
    21. Alan Schwartz, 2004. "The Law and Economics of Costly Contracting," The Journal of Law, Economics, and Organization, Oxford University Press, vol. 20(1), pages 2-31, April.

    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:matcom:v:81:y:2010:i:1:p:52-61. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.