IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v110y2015icp33-39.html
   My bibliography  Save this article

Dynamics in piecewise linear and continuous models of complex switching networks

Author

Listed:
  • Shahrear, Pabel
  • Glass, Leon
  • Wilds, Roy
  • Edwards, Rod

Abstract

Activities of genes are controlled in a combinatorial fashion by the concentrations of chemical called transcription factors. We model this type of network by piecewise linear differential equations formed by embedding a logical switching network in a differential equation. We generate continuous nonlinear equations by replacing the step function discontinuities in the piecewise linear equations by sigmoidal control functions. As the sigmoidal functions become steep, the continuous equations approach piecewise linear differential equations. We carry out numerical studies of the continuous and piecewise linear equations for a 4-dimensional example with particularly interesting and complex behavior, showing that the dynamics in the continuous equation approaches those in the piecewise linear equation as the sigmoids become steep.

Suggested Citation

  • Shahrear, Pabel & Glass, Leon & Wilds, Roy & Edwards, Rod, 2015. "Dynamics in piecewise linear and continuous models of complex switching networks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 110(C), pages 33-39.
  • Handle: RePEc:eee:matcom:v:110:y:2015:i:c:p:33-39
    DOI: 10.1016/j.matcom.2013.12.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475413003054
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.matcom.2013.12.002?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. Anonymous, 2013. "Introduction to the Issue," Journal of Wine Economics, Cambridge University Press, vol. 8(3), pages 243-243, December.
    2. Gernot Grabher & Walter W. Powell (ed.), 2004. "Networks," Books, Edward Elgar Publishing, volume 0, number 2771.
    3. Edwards, Roderick & Farcot, Etienne & Foxall, Eric, 2012. "Explicit construction of chaotic attractors in Glass networks," Chaos, Solitons & Fractals, Elsevier, vol. 45(5), pages 666-680.
    4. Anonymous, 2013. "Introduction to the Issue," Journal of Wine Economics, Cambridge University Press, vol. 8(2), pages 129-130, November.
    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. Ranjana Raghunathan, 2022. "Everyday Intimacies and Inter-Ethnic Relationships: Tracing Entanglements of Gender and Race in Multicultural Singapore," Sociological Research Online, , vol. 27(1), pages 77-94, March.
    2. Balint, T. & Lamperti, F. & Mandel, A. & Napoletano, M. & Roventini, A. & Sapio, A., 2017. "Complexity and the Economics of Climate Change: A Survey and a Look Forward," Ecological Economics, Elsevier, vol. 138(C), pages 252-265.
    3. Lamperti, Francesco & Bosetti, Valentina & Roventini, Andrea & Tavoni, Massimo & Treibich, Tania, 2021. "Three green financial policies to address climate risks," Journal of Financial Stability, Elsevier, vol. 54(C).
    4. Songsore, Emmanuel & Buzzelli, Michael, 2014. "Social responses to wind energy development in Ontario: The influence of health risk perceptions and associated concerns," Energy Policy, Elsevier, vol. 69(C), pages 285-296.
    5. Tapsuwan, Sorada & Polyakov, Maksym & Bark, Rosalind & Nolan, Martin, 2015. "Valuing the Barmah–Millewa Forest and in stream river flows: A spatial heteroskedasticity and autocorrelation consistent (SHAC) approach," Ecological Economics, Elsevier, vol. 110(C), pages 98-105.
    6. Omar Al-Ubaydli & John List & Claire Mackevicius & Min Sok Lee & Dana Suskind, 2019. "How Can Experiments Play a Greater Role in Public Policy? 12 Proposals from an Economic Model of Scaling," Artefactual Field Experiments 00679, The Field Experiments Website.
    7. Nepomuceno, Marcelo Vinhal & Laroche, Michel, 2015. "The impact of materialism and anti-consumption lifestyles on personal debt and account balances," Journal of Business Research, Elsevier, vol. 68(3), pages 654-664.
    8. Bertschek, Irene & Kesler, Reinhold, 2022. "Let the user speak: Is feedback on Facebook a source of firms’ innovation?," Information Economics and Policy, Elsevier, vol. 60(C).
    9. Avelino, Flor & Wittmayer, Julia M. & Pel, Bonno & Weaver, Paul & Dumitru, Adina & Haxeltine, Alex & Kemp, René & Jørgensen, Michael S. & Bauler, Tom & Ruijsink, Saskia & O'Riordan, Tim, 2019. "Transformative social innovation and (dis)empowerment," Technological Forecasting and Social Change, Elsevier, vol. 145(C), pages 195-206.
    10. Gigi Foster, 2020. "The behavioural economics of government responses to COVID-19," Journal of Behavioral Economics for Policy, Society for the Advancement of Behavioral Economics (SABE), vol. 4(S3), pages 11-43, December.
    11. Audoly, Richard & Vogt-Schilb, Adrien & Guivarch, Céline & Pfeiffer, Alexander, 2018. "Pathways toward zero-carbon electricity required for climate stabilization," Applied Energy, Elsevier, vol. 225(C), pages 884-901.
    12. Gerards, Ruud & Welters, Ricardo, 2016. "Impact of financial pressure on unemployed job search, job find success and job quality," ROA Research Memorandum 008, Maastricht University, Research Centre for Education and the Labour Market (ROA).
    13. Cairns, George & Wright, George & Fairbrother, Peter, 2016. "Promoting articulated action from diverse stakeholders in response to public policy scenarios: A case analysis of the use of ‘scenario improvisation’ method," Technological Forecasting and Social Change, Elsevier, vol. 103(C), pages 97-108.
    14. Vasile-Daniel Păvăloaia & Elena-Mădălina Teodor & Doina Fotache & Magdalena Danileţ, 2019. "Opinion Mining on Social Media Data: Sentiment Analysis of User Preferences," Sustainability, MDPI, vol. 11(16), pages 1-21, August.
    15. Cailong Xu & Ruidong Li & Wenwen Song & Tingting Wu & Shi Sun & Shuixiu Hu & Tianfu Han & Cunxiang Wu, 2021. "Responses of Branch Number and Yield Component of Soybean Cultivars Tested in Different Planting Densities," Agriculture, MDPI, vol. 11(1), pages 1-12, January.
    16. Romaniuk, Jenni & Nenycz-Thiel, Magda, 2016. "Lapsed buyers' durable brand consideration in emerging markets," Journal of Business Research, Elsevier, vol. 69(9), pages 3645-3651.
    17. Caitlin Robinson & Stefan Bouzarovski & Sarah Lindley, 2018. "Underrepresenting neighbourhood vulnerabilities? The measurement of fuel poverty in England," Environment and Planning A, , vol. 50(5), pages 1109-1127, August.
    18. Michaela Haase & Emmanuel Raufflet, 2017. "Ideologies in Markets, Organizations, and Business Ethics: Drafting a Map: Introduction to the Special Issue," Journal of Business Ethics, Springer, vol. 142(4), pages 629-639, June.
    19. Rafael Alcadipani & Cíntia Rodrigues Oliveira Medeiros, 2020. "When Corporations Cause Harm: A Critical View of Corporate Social Irresponsibility and Corporate Crimes," Journal of Business Ethics, Springer, vol. 167(2), pages 285-297, November.
    20. Mansoora Ahmed & Sun Zehou & Syed Ali Raza & Muhammad Asif Qureshi & Sara Qamar Yousufi, 2020. "Impact of CSR and environmental triggers on employee green behavior: The mediating effect of employee well‐being," Corporate Social Responsibility and Environmental Management, John Wiley & Sons, vol. 27(5), pages 2225-2239, September.

    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:110:y:2015:i:c:p:33-39. 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.