IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v387y2008i11p2511-2518.html
   My bibliography  Save this article

Towards possible q-generalizations of the Malthus and Verhulst growth models

Author

Listed:
  • Strzałka, Dominik
  • Grabowski, Franciszek

Abstract

Tsallis entropy introduced in 1988 based on the equation Sq=1−∑ipiqq−1 has been considered to obtain new possibilities for constructing a generalized thermodynamical basis for statistical physics, expanding classical Boltzmann–Gibbs thermodynamics for non-equilibrium states. During the last two decades this q-generalized theory has been successfully applied to a considerable amount of physically interesting complex phenomena. The authors wish to present a mathematical analysis of the possible q-generalizations of the Malthus and the Verhulst growth models based on Tsallis definitions of the q-logarithm and the q-exponential.

Suggested Citation

  • Strzałka, Dominik & Grabowski, Franciszek, 2008. "Towards possible q-generalizations of the Malthus and Verhulst growth models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(11), pages 2511-2518.
    • Handle: RePEc:eee:phsmap:v:387:y:2008:i:11:p:2511-2518
    DOI: 10.1016/j.physa.2007.12.014
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437107013295
    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.2007.12.014?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. Barabási, Albert-László & Albert, Réka & Jeong, Hawoong, 1999. "Mean-field theory for scale-free random networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 272(1), pages 173-187.
    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. Ribeiro, Fabiano L. & Ribeiro, Kayo N., 2015. "A one dimensional model of population growth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 434(C), pages 201-210.
    2. Cabella, Brenno Caetano Troca & Ribeiro, Fabiano & Martinez, Alexandre Souto, 2012. "Effective carrying capacity and analytical solution of a particular case of the Richards-like two-species population dynamics model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1281-1286.

    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. Liang, Wei & Shi, Yuming & Huang, Qiuling, 2014. "Modeling the Chinese language as an evolving network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 393(C), pages 268-276.
    2. Yan Qiang & Bo Pei & Weili Wu & Juanjuan Zhao & Xiaolong Zhang & Yue Li & Lidong Wu, 2014. "Improvement of path analysis algorithm in social networks based on HBase," Journal of Combinatorial Optimization, Springer, vol. 28(3), pages 588-599, October.
    3. Pi, Xiaochen & Tang, Longkun & Chen, Xiangzhong, 2021. "A directed weighted scale-free network model with an adaptive evolution mechanism," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 572(C).
    4. Stephanie Rend'on de la Torre & Jaan Kalda & Robert Kitt & Juri Engelbrecht, 2016. "On the topologic structure of economic complex networks: Empirical evidence from large scale payment network of Estonia," Papers 1602.04352, arXiv.org.
    5. Yoshiharu Maeno & Kenji Nishiguchi & Satoshi Morinaga & Hirokazu Matsushima, 2014. "Impact of credit default swaps on financial contagion," Papers 1411.1356, arXiv.org.
    6. Rabbani, Fereshteh & Khraisha, Tamer & Abbasi, Fatemeh & Jafari, Gholam Reza, 2021. "Memory effects on link formation in temporal networks: A fractional calculus approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 564(C).
    7. Gabrielle Demange, 2012. "On the influence of a ranking system," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(2), pages 431-455, July.
    8. Cheng, Ranran & Peng, Mingshu & Yu, Weibin, 2014. "Pinning synchronization of delayed complex dynamical networks with nonlinear coupling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 413(C), pages 426-431.
    9. Tsao, J.Y. & Boyack, K.W. & Coltrin, M.E. & Turnley, J.G. & Gauster, W.B., 2008. "Galileo's stream: A framework for understanding knowledge production," Research Policy, Elsevier, vol. 37(2), pages 330-352, March.
    10. Pier Paolo Saviotti, 2011. "Knowledge, Complexity and Networks," Chapters, in: Cristiano Antonelli (ed.), Handbook on the Economic Complexity of Technological Change, chapter 6, Edward Elgar Publishing.
    11. Duan, Shuyu & Wen, Tao & Jiang, Wen, 2019. "A new information dimension of complex network based on Rényi entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 516(C), pages 529-542.
    12. Sanjeev Goyal & Marco J. van der Leij & José Luis Moraga-Gonzalez, 2006. "Economics: An Emerging Small World," Journal of Political Economy, University of Chicago Press, vol. 114(2), pages 403-432, April.
    13. Silva, F.N. & Viana, M.P. & Travençolo, B.A.N. & Costa, L. da F., 2011. "Investigating relationships within and between category networks in Wikipedia," Journal of Informetrics, Elsevier, vol. 5(3), pages 431-438.
    14. Dávid Csercsik & Sándor Imre, 2017. "Cooperation and coalitional stability in decentralized wireless networks," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 64(4), pages 571-584, April.
    15. Chung-Yuan Huang & Chuen-Tsai Sun & Hsun-Cheng Lin, 2005. "Influence of Local Information on Social Simulations in Small-World Network Models," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 8(4), pages 1-8.
    16. Sun, Bingbin & Yao, Jialing & Xi, Lifeng, 2019. "Eigentime identities of fractal sailboat networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 520(C), pages 338-349.
    17. Waseem Akram & Muaz Niazi & Laszlo Barna Iantovics & Athanasios V. Vasilakos, 2019. "Towards Agent-Based Model Specification of Smart Grid: A Cognitive Agent-Based Computing Approach," Interdisciplinary Description of Complex Systems - scientific journal, Croatian Interdisciplinary Society Provider Homepage: http://indecs.eu, vol. 17(3-B), pages 546-585.
    18. Luka Kronegger & Anuška Ferligoj & Patrick Doreian, 2011. "On the dynamics of national scientific systems," Quality & Quantity: International Journal of Methodology, Springer, vol. 45(5), pages 989-1015, August.
    19. Yang, Xu-Hua & Lou, Shun-Li & Chen, Guang & Chen, Sheng-Yong & Huang, Wei, 2013. "Scale-free networks via attaching to random neighbors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(17), pages 3531-3536.
    20. Legara, Erika Fille & Monterola, Christopher & Juanico, Dranreb Earl & Litong-Palima, Marisciel & Saloma, Caesar, 2008. "Earning potential in multilevel marketing enterprises," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(19), pages 4889-4895.

    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:387:y:2008:i:11:p:2511-2518. 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.