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On rational systems in the plane. I. Riccati Cases
Gabriel Lugo, Frank J. Palladino
This paper is the first in a series of papers which will address, on a case by case basis, the special cases of the following rational system in the plane, labeled system #11. $$x_…
On competitive discrete systems in the plane. I. Invariant Manifolds
Gabriel Lugo, Frank J. Palladino
Let be a competitive map on a rectangular region . The main results of this paper give conditions which guarantee the existence of an invariant…
On a second-order rational difference equation and a rational system
Gabriel Lugo, Frank J. Palladino
We give a complete description of the qualitative behavior of the second-order rational difference equation #166. We also establish the boundedness character for the rational syste…
Some boundedness results for systems of two rational difference equations
Gabriel Lugo, Frank J. Palladino
We study kth order systems of two rational difference equations $$x_n=\frac{α+\sum^{k}_{i=1}β_{i}x_{n-i} + \sum^{k}_{i=1}γ_{i}y_{n-i}}{A+\sum^{k}_{j=1}B_{j}x_{n-j} + \sum^{k}_{j=1}…