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Open Access Research Article

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

RanaD Parshad1* and JuanB Gutierrez2

Author Affiliations

1 Department of Mathematics and Computer Science, Clarkson University, Potsdam, NY 13676, USA

2 Mathematical Biosciences Institute, Ohio State University, Columbus, OH 43210, USA

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Boundary Value Problems 2010, 2010:405816  doi:10.1155/2010/405816


The electronic version of this article is the complete one and can be found online at: http://www.boundaryvalueproblems.com/content/2010/1/405816


Received:14 July 2010
Accepted:2 November 2010
Published:22 November 2010

© 2010 Rana D. Parshad and Juan B. Gutierrez.

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.

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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