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Vector growth universalities

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  • Barberis, L.
  • Condat, C.A.
  • Román, P.

Abstract

A formalism to describe the interactive growth of two or more organisms in a given environment is presented. This is a vector generalization of the scheme developed by Castorina et al. [1] to classify and interpret non-linear ontogenetic growth formulas, which can be applied to such complex self-organizing systems as solid tumors. A theorem that leads to the explicit solutions of the resulting equations is proven. These solutions can describe synergetic, antagonistic, and cooperative growth, and can be applied to both biological and ecological problems.

Suggested Citation

  • Barberis, L. & Condat, C.A. & Román, P., 2011. "Vector growth universalities," Chaos, Solitons & Fractals, Elsevier, vol. 44(12), pages 1100-1105.
    • Handle: RePEc:eee:chsofr:v:44:y:2011:i:12:p:1100-1105
    DOI: 10.1016/j.chaos.2011.09.007
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    1. Martinez, Alexandre Souto & González, Rodrigo Silva & Terçariol, César Augusto Sangaletti, 2008. "Continuous growth models in terms of generalized logarithm and exponential functions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(23), pages 5679-5687.
    2. Antonio S Gliozzi & Caterina Guiot & Pier Paolo Delsanto, 2009. "A New Computational Tool for the Phenomenological Analysis of Multipassage Tumor Growth Curves," PLOS ONE, Public Library of Science, vol. 4(4), pages 1-7, April.
    3. Delsanto, Pier Paolo & Gliozzi, Antonio S. & Bruno, Caterina L.E. & Pugno, Nicola & Carpinteri, Alberto, 2009. "Scaling laws and fractality in the framework of a phenomenological approach," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2782-2786.
    4. Menchón, S.A. & Condat, C.A., 2011. "Quiescent cells: A natural way to resist chemotherapy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(20), pages 3354-3361.
    5. Alexandre Souto Martinez & Rodrigo Silva Gonzalez & Cesar Augusto Sangaletti Tercariol, 2008. "Continuous growth models in terms of generalized logarithm and exponential functions," Papers 0803.2635, arXiv.org, revised May 2008.
    6. Geoffrey B. West & James H. Brown & Brian J. Enquist, 2001. "A general model for ontogenetic growth," Nature, Nature, vol. 413(6856), pages 628-631, October.
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    1. Barberis, L. & Condat, C.A., 2012. "Describing interactive growth using vector universalities," Ecological Modelling, Elsevier, vol. 227(C), pages 56-63.

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