Study of the stability of a system of difference equations using Centre Manifold Theory

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• 作者：N. Psarros ^{nikosnpsarros@hotmail.com" class="auth_mail" title="E-mail the corresponding author} ; G. Papaschinopoulos ; ^{gpapas@env.duth.gr" class="auth_mail" title="E-mail the corresponding author} ; C.J. Schinas ^{cschinas@ee.duth.gr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Difference equations ; Stability ; Centre manifold
• 刊名：Applied Mathematics Letters
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：64
• 期：Complete
• 页码：185-192
• 全文大小：752 K

文摘

We study the stability of the zero equilibrium of the following system of difference equations, which is a natural extension of an one-dimensional biologicalmodel: where source">a₁$a_1$, source">a₂$a_2$, source">a₃$a_3$, 32804bd62a3" title="Click to view the MathML source">b₁$b_1$, source">b₂$b_2$, source">b₃$b_3$ are real constants and the initial values conditions source">x₀$x_0$, source">y₀$y_0$ and source">z₀$z_0$ are real numbers. The stability of those systems in the special case when one of the eigenvalues has absolute value equal to 1 and the other two eigenvalues have absolute value less than 1, using centre manifold theory, is investigated.