IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v464y2016icp1-10.html
   My bibliography  Save this article

Diffusion of innovations dynamics, biological growth and catenary function

Author

Listed:
  • Guseo, Renato

Abstract

The catenary function has a well-known role in determining the shape of chains and cables supported at their ends under the force of gravity. This enables design using a specific static equilibrium over space. Its reflected version, the catenary arch, allows the construction of bridges and arches exploiting the dual equilibrium property under uniform compression. In this paper, we emphasize a further connection with well-known aggregate biological growth models over time and the related diffusion of innovation key paradigms (e.g., logistic and Bass distributions over time) that determine self-sustaining evolutionary growth dynamics in naturalistic and socio-economic contexts. Moreover, we prove that the ‘local entropy function’, related to a logistic distribution, is a catenary and vice versa. This special invariance may be explained, at a deeper level, through the Verlinde’s conjecture on the origin of gravity as an effect of the entropic force.

Suggested Citation

  • Guseo, Renato, 2016. "Diffusion of innovations dynamics, biological growth and catenary function," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 464(C), pages 1-10.
    • Handle: RePEc:eee:phsmap:v:464:y:2016:i:c:p:1-10
    DOI: 10.1016/j.physa.2016.07.015
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437116304460
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2016.07.015?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. Guseo, Renato & Guidolin, Mariangela, 2010. "Cellular Automata with network incubation in information technology diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(12), pages 2422-2433.
    2. Frank M. Bass & Trichy V. Krishnan & Dipak C. Jain, 1994. "Why the Bass Model Fits without Decision Variables," Marketing Science, INFORMS, vol. 13(3), pages 203-223.
    3. Frank M. Bass, 1969. "A New Product Growth for Model Consumer Durables," Management Science, INFORMS, vol. 15(5), pages 215-227, January.
    4. Renato Guseo & Mariangela Guidolin, 2008. "Cellular automata and Riccati equation models for diffusion of innovations," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 17(3), pages 291-308, July.
    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. Guseo, Renato & Mortarino, Cinzia, 2012. "Sequential market entries and competition modelling in multi-innovation diffusions," European Journal of Operational Research, Elsevier, vol. 216(3), pages 658-667.
    2. Guseo, Renato & Guidolin, Mariangela, 2010. "Cellular Automata with network incubation in information technology diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(12), pages 2422-2433.
    3. Guseo, Renato & Guidolin, Mariangela, 2015. "Heterogeneity in diffusion of innovations modelling: A few fundamental types," Technological Forecasting and Social Change, Elsevier, vol. 90(PB), pages 514-524.
    4. Guseo, Renato & Mortarino, Cinzia & Darda, Md Abud, 2015. "Homogeneous and heterogeneous diffusion models: Algerian natural gas production," Technological Forecasting and Social Change, Elsevier, vol. 90(PB), pages 366-378.
    5. Guseo, Renato & Schuster, Reinhard, 2021. "Modelling dynamic market potential: Identifying hidden automata networks in the diffusion of pharmaceutical drugs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 581(C).
    6. Yuri Peers & Dennis Fok & Philip Hans Franses, 2012. "Modeling Seasonality in New Product Diffusion," Marketing Science, INFORMS, vol. 31(2), pages 351-364, March.
    7. Constanza Fosco, 2012. "Spatial Difusion and Commuting Flows," Documentos de Trabajo en Economia y Ciencia Regional 30, Universidad Catolica del Norte, Chile, Department of Economics, revised Sep 2012.
    8. Vakratsas, Demetrios & Kolsarici, Ceren, 2008. "A dual-market diffusion model for a new prescription pharmaceutical," International Journal of Research in Marketing, Elsevier, vol. 25(4), pages 282-293.
    9. Al-Alawi, Baha M. & Bradley, Thomas H., 2013. "Review of hybrid, plug-in hybrid, and electric vehicle market modeling Studies," Renewable and Sustainable Energy Reviews, Elsevier, vol. 21(C), pages 190-203.
    10. Trichy V. Krishnan & Frank M. Bass & Dipak C. Jain, 1999. "Optimal Pricing Strategy for New Products," Management Science, INFORMS, vol. 45(12), pages 1650-1663, December.
    11. Peters, Kay & Albers, Sönke & Kumar, V., 2008. "Is there more to international Diffusion than Culture? An investigation on the Role of Marketing and Industry Variables," EconStor Preprints 27678, ZBW - Leibniz Information Centre for Economics.
    12. Tunstall, Thomas, 2015. "Iterative Bass Model forecasts for unconventional oil production in the Eagle Ford Shale," Energy, Elsevier, vol. 93(P1), pages 580-588.
    13. Jonathan Lee & Peter Boatwright & Wagner A. Kamakura, 2003. "A Bayesian Model for Prelaunch Sales Forecasting of Recorded Music," Management Science, INFORMS, vol. 49(2), pages 179-196, February.
    14. Orbach Yair & Fruchter Gila E., 2010. "A Utility-Based Diffusion Model Applied to the Digital Camera Case," Review of Marketing Science, De Gruyter, vol. 8(1), pages 1-28, June.
    15. Krishnamoorthy, Anand & Prasad, Ashutosh & Sethi, Suresh P., 2010. "Optimal pricing and advertising in a durable-good duopoly," European Journal of Operational Research, Elsevier, vol. 200(2), pages 486-497, January.
    16. T. Marshalkina V. & Т. Маршалкина В., 2015. "Модели Прогнозирования Спроса На Инновационную Продукцию // Models For Innovative Products Demand," Финансы: теория и практика/Finance: Theory and Practice // Finance: Theory and Practice, ФГОБУВО Финансовый университет при Правительстве Российской Федерации // Financial University under The Government of Russian Federation, issue 6, pages 171-178.
    17. Trichy V. Krishnan & Dipak C. Jain, 2006. "Optimal Dynamic Advertising Policy for New Products," Management Science, INFORMS, vol. 52(12), pages 1957-1969, December.
    18. Claudia Furlan & Cinzia Mortarino, 2020. "Comparison among simultaneous confidence regions for nonlinear diffusion models," Computational Statistics, Springer, vol. 35(4), pages 1951-1991, December.
    19. Inseong Song & Pradeep Chintagunta, 2003. "A Micromodel of New Product Adoption with Heterogeneous and Forward-Looking Consumers: Application to the Digital Camera Category," Quantitative Marketing and Economics (QME), Springer, vol. 1(4), pages 371-407, December.
    20. Herbert Dawid & Reinhold Decker & Thomas Hermann & Hermann Jahnke & Wilhelm Klat & Rolf König & Christian Stummer, 2017. "Management science in the era of smart consumer products: challenges and research perspectives," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 25(1), pages 203-230, March.

    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:phsmap:v:464:y:2016:i:c:p:1-10. 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/physica-a-statistical-mechpplications/ .

    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.