On systems of rational difference equations and periodic tetrachotomies

Details On systems of rational difference equations and periodic tetrachotomies On systems of rational difference equations and periodic tetrachotomies

2009-09-23

arxiv.org/abs/0909.4308v3

Mathematics

Dynamical Systems

The earlier work required that the matrix be Hermitian and so did not give the full characterization of qualitative behavior.

Scientific paper

We study the following system of two rational difference equations x_n=({\beta}_k x_(n-k)+{\gamma}_k y_(n-k))/(A+\Sigma_(j=1)^l[B_j x_(n-j) ]+\Sigma_(j=1)^l[C_j y_(n-j) ]), n \in N, y_n=({\delta}_k x_(n-k)+\in_k y_(n-k))/(q+\Sigma_(j=1)^l[D_j x_(n-j) ]+\Sigma_(j=1)^l[E_j y_(n-j) ]), n\in N, with nonnegative parameters and nonnegative initial conditions. We assume that B_j=C_j=D_j=E_j=0 for j=k, 2k, 3k, ...and establish the existence of periodic tetrachotomy behavior which depends on a 2X2 matrix with entries {\beta}_k, {\gamma}_k, {\delta}_k, and \in_k.

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