关于有理差分方程组与周期四分法
动力系统
2011-02-02 v3
摘要
我们研究以下两个有理差分方程组成的系统：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，其中参数和初始条件均为非负。我们假设对于j=k, 2k, 3k, ...有B_j=C_j=D_j=E_j=0，并建立了依赖于一个元素为{\beta}_k, {\gamma}_k, {\delta}_k和\in_k的2X2矩阵的周期四分法行为的存在性。
引用
@article{arxiv.0909.4308,
title = {On systems of rational difference equations and periodic tetrachotomies},
author = {Frank J. Palladino},
journal= {arXiv preprint arXiv:0909.4308},
year = {2011}
}
备注
The earlier work required that the matrix be Hermitian and so did not give the full characterization of qualitative behavior. This version improves on the work posted prior and gives the complete picture in this case