This dissertation presents and evaluates a theoretical method of eradication of invasive species through the use of Trojan Y chromosomes. The mathematical analysis of the Trojan Y chromosome eradication strategy is presented for the ODE case and the PDE case in [special characters omitted]. It is shown that is possible to cause local extinction of species that have XY sex determination systems as long as they are susceptible to sex reversal. The existence of global attractors is shown for this system, and global attractors are proposed as descriptors of the dynamics of the infinite dimensional system. The case of Poecilia formosa is studied as a natural case of Trojan X chromosomes; it is shown in this case that the combination of stochastic-dependent dissipation and high sensitivity to perturbations can lead to coexistence of P. formosa and P. mexicana . Similarities between the Trojan X chromosomes and Trojan Y chromosomes cases indicate that local extinction could occur in practice for the latter.