Stability of two 3 × 3 close‐to‐cyclic systems of exponential difference equations
Stability of two 3 × 3 close‐to‐cyclic systems of exponential difference equations
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DOI：
10.1002/mma.5256
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发表时间：
2018-09
影响因子：
2.9
通讯作者：
Chrysoula Mylona;N. Psarros;G. Papaschinopoulos;C. Schinas
中科院分区：
文献类型：
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作者：
Chrysoula Mylona;N. Psarros;G. Papaschinopoulos;C. Schinas
本文研究如下差分方程组的零平衡点的稳定性：xn+1= a1 xn + b1 yne −xn，yn+1= a2 yn + b2 zne −yn，zn+1= a3 zn + b3 xne −zn，xn+1= a1 yn + b1 xne −yn，yn+1= a2 zn + b2 yne −zn，zn+1= a3 xn + b3 zne −xn，其中a1，a2，a3，b1，b2，b3是真实的常数，初值x0，y0，z0是真实的数.我们利用中心流形理论研究了当相应线性化系统的系数矩阵的特征值之一等于−1且其余特征值的绝对值小于1的特殊情况下系统的稳定性。
In this paper, we study the stability of the zero equilibria of the following systems of difference equations: xn+1=a1xn+b1yne−xn,yn+1=a2yn+b2zne−yn,zn+1=a3zn+b3xne−zn, xn+1=a1yn+b1xne−yn,yn+1=a2zn+b2yne−zn,zn+1=a3xn+b3zne−xn, where a1, a2, a3, b1, b2, and b3 are real constants, and the initial values x0, y0, and z0 are real numbers. We study the stability of those systems in the special case when one of the eigenvalues of the coefficient matrix of the corresponding linearized systems is equal to −1 and the remaining eigenvalues have absolute value less than 1, using centre manifold theory.