Frank J. Palladino
On a second-order rational difference equation and a rational system.
Tue, 02/07/2012 - 15:01 — SomNambulAuthors: Frank J. Palladino, Gabriel Lugo
Subjects: Dynamical Systems
AbstractWe 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 system in the plane #(8,30).On Half Cauchy Sequences.
Thu, 02/24/2011 - 16:01 — SomNambulAuthors: Frank J. Palladino
Subjects: Classical Analysis and ODEs
AbstractIn this note we introduce and define half Cauchy sequences. We prove that a
sequence of real numbers is convergent if and only if it is bounded and half
Cauchy. We also provide an example of how the concept may be used.Some boundedness results for systems of two rational difference equations.
Thu, 10/01/2009 - 00:35 — SomNambulAuthors: Frank J. Palladino, Gabriel Lugo
Subjects: Dynamical Systems
AbstractWe study kth order systems of two rational difference equations
$$x_n=\frac{\alpha+\sum^{k}_{i=1}\beta_{i}x_{n-i} +
\sum^{k}_{i=1}\gamma_{i}y_{n-i}}{A+\sum^{k}_{j=1}B_{j}x_{n-j} +
\sum^{k}_{j=1}C_{j}y_{n-j}},\quad n\in\mathbb{N},$$
$$y_n=\frac{p+\sum^{k}_{i=1}\delta_{i}x_{n-i} +
\sum^{k}_{i=1}\epsilon_{i}y_{n-i}}{q+\sum^{k}_{j=1}D_{j}x_{n-j} +
\sum^{k}_{j=1}E_{j}y_{n-j}},\quad n\in\mathbb{N}.$$ In particular we assume
non-negative parameters and non-negative initial conditions.On systems of rational difference equations and periodic tetrachotomies.
Sat, 09/26/2009 - 04:10 — SomNambulAuthors: Frank J. Palladino
Subjects: Dynamical Systems
AbstractWe study the kth order system of two rational difference equations
$$x_n=\frac{\beta_k x_{n-k} +\gamma_k y_{n-k}} {1+\sum_{j=1}^{k-1}B_j x_{n-j}
+ \sum_{j=1}^{k-1}C_{j}y_{n-j}}, n\in\mathbb{N},$$$$y_{n}=\frac{\delta_k x_{n-k} +\epsilon_k y_{n-k}} {1+\sum_{j=1}^{k-1}D_j
x_{n-j} + \sum_{j=1}^{k-1}E_j y_{n-j}}, n\in\mathbb{N},$$ with nonnegative
parameters and nonnegative initial conditions.We establish the existence of periodic tetrachotomy behavior which depends on
the matrix $$(\begin{array}{cc} \beta_{k} & \gamma_k
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