On the global attractor of the Trojan Y Chromosome model

Rana D. Parshad; Juan B. Gutierrez

doi:10.3934/cpaa.2011.10.339

Article Contents

2011, Volume 10, Issue 1: 339-359. Doi: 10.3934/cpaa.2011.10.339

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On the global attractor of the Trojan Y Chromosome model

Rana D. Parshad^1, and
Juan B. Gutierrez^2,

1.
Clarkson University, Department of Mathematics & Computer Science, 106 Technology Advancement Center, Potsdam, NY 13676
2.
Mathematical Biosciences Institute, The Ohio State University, 1735 Neil Ave, 3rd Floor, Columbus, OH 43210

Received: December 31, 2009

Revised: May 31, 2010

Published: December 2010

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Abstract

We consider the Trojan Y Chromosome (TYC) model for eradication of invasive species in population dynamics. We present global estimates for the TYC system in a spatial domain. In this work we prove the existence of a global attractor for the system. We derive uniform estimates to tackle the question of asymptotic compactness of the semi-group for the TYC model in $H^2(\Omega)$. This along with the existence of a bounded absorbing set, which we also derive, demonstrates the existence of a global attractor for the TYC model. The present analysis reveals that extinction of an invasive species is always possible to achieve irrespective of geometric considerations of the domain. This result is valid for TYC systems in which advection is negligible. This theoretical work lays the foundation for experimental studies of the application of the TYC eradication strategy in spatial ecology, since the outcome is in principle guaranteed.

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Mathematics Subject Classification: Primary: 35B40, 37L300; Secondary: 92D25.

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