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Báo cáo hóa học: " Research Article Dynamics of a Rational System of Difference Equations in the Plane"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Dynamics of a Rational System of Difference Equations in the Plane | Hindawi Publishing Corporation Advances in Difference Equations Volume 2011 Article ID 958602 17 pages doi 10.1155 2011 958602 Research Article Dynamics of a Rational System of Difference Equations in the Plane Ignacio Bajo 1 Daniel Franco 2 and Juan Periin2 1 Departamento de Matemática Aplicada II E.T.S.E. Telecomunicacion Universidade de Vigo Campus Marcosende 36310 Vigo Spain 2 Departamento de Matemứtica Aplicada E.T.S.I. Industriales UNED C Juan del Rosal 12 28040 Madrid Spain Correspondence should be addressed to Juan Periin jperan@ind.uned.es Received 10 December 2010 Accepted 21 February 2011 Academic Editor Istvan Gyori Copyright 2011 Ignacio Bajo etal. 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 work is properly cited. We consider a rational system of first-order difference equations in the plane with four parameters such that all fractions have a common denominator. We study for the different values of the parameters the global and local properties of the system. In particular we discuss the boundedness and the asymptotic behavior of the solutions the existence of periodic solutions and the stability of equilibria. 1. Introduction In recent years rational difference equations have attracted the attention of many researchers for varied reasons. On the one hand they provide examples of nonlinear equations which are in some cases treatable but whose dynamics present some new features with respect to the linear case. On the other hand rational equations frequently appear in some biological models and hence their study is of interest also due to their applications. A good example of both facts is Ricatti difference equations the richness of the dynamics of Ricatti equations is very well-known see e.g. 1 2 and a particular case of these equations provides the classical Beverton-Holt model on the dynamics of exploited .