On the Well Posedness and Refined Estimates for the Global Attractor of the TYC Model

  • RanaD Parshad1Email author and

    Affiliated with

    • JuanB Gutierrez2

      Affiliated with

      Boundary Value Problems20102010:405816

      DOI: 10.1155/2010/405816

      Received: 14 July 2010

      Accepted: 2 November 2010

      Published: 22 November 2010

      Abstract

      The Trojan Y Chromosome strategy (TYC) is a theoretical method for eradication of invasive species. It requires constant introduction of artificial individuals into a target population, causing a shift in the sex ratio that ultimately leads to local extinction. In this work we demonstrate the existence of a unique weak solution to the infinite dimensional TYC system. Furthermore, we obtain improved estimates on the upper bounds for the Hausdorff and fractal dimensions of the global attractor of the TYC system, via the use of weighted Sobolev spaces. These results confirm that the TYC eradication strategy is a sound theoretical method of eradication of invasive species in a spatial setting. It also provides a solid ground for experiments in silico and validates the use of the TYC strategy in vivo.

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      Authors’ Affiliations

      (1)
      Department of Mathematics and Computer Science, Clarkson University
      (2)
      Mathematical Biosciences Institute, Ohio State University

      Copyright

      © R. D. Parshad and J. B. Gutierrez. 2010

      This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original paper is properly cited.