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

详细信息    查看全文

• 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 class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0893965916302750&_mathId=si3.gif&_user=111111111&_pii=S0893965916302750&_rdoc=1&_issn=08939659&md5=8f955869afeb23a2b2f473cf32bec74b" title="Click to view the MathML source">a₁class="mathContainer hidden">class="mathCode">$a_1$, class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0893965916302750&_mathId=si4.gif&_user=111111111&_pii=S0893965916302750&_rdoc=1&_issn=08939659&md5=7c566ad9ed0e6d26164c2e0a702057be" title="Click to view the MathML source">a₂class="mathContainer hidden">class="mathCode">$a_2$, class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0893965916302750&_mathId=si5.gif&_user=111111111&_pii=S0893965916302750&_rdoc=1&_issn=08939659&md5=a4799aeb699a30fa775abd016d434320" title="Click to view the MathML source">a₃class="mathContainer hidden">class="mathCode">$a_3$, class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0893965916302750&_mathId=si6.gif&_user=111111111&_pii=S0893965916302750&_rdoc=1&_issn=08939659&md5=99ff3bf90a5e37197502932804bd62a3" title="Click to view the MathML source">b₁class="mathContainer hidden">class="mathCode">$b_1$, class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0893965916302750&_mathId=si7.gif&_user=111111111&_pii=S0893965916302750&_rdoc=1&_issn=08939659&md5=2749d696ff017c52f12d39dc437a1b16" title="Click to view the MathML source">b₂class="mathContainer hidden">class="mathCode">$b_2$, class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0893965916302750&_mathId=si8.gif&_user=111111111&_pii=S0893965916302750&_rdoc=1&_issn=08939659&md5=867a949030655d4ff4c90881ffa2a8f9" title="Click to view the MathML source">b₃class="mathContainer hidden">class="mathCode">$b_3$ are real constants and the initial values conditions class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0893965916302750&_mathId=si9.gif&_user=111111111&_pii=S0893965916302750&_rdoc=1&_issn=08939659&md5=b99ce840cf43effad7b2681a256d557c" title="Click to view the MathML source">x₀class="mathContainer hidden">class="mathCode">$x_0$, class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0893965916302750&_mathId=si10.gif&_user=111111111&_pii=S0893965916302750&_rdoc=1&_issn=08939659&md5=6ac2315f925119f1818bc84ee2690c4a" title="Click to view the MathML source">y₀class="mathContainer hidden">class="mathCode">$y_0$ and class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0893965916302750&_mathId=si11.gif&_user=111111111&_pii=S0893965916302750&_rdoc=1&_issn=08939659&md5=c776f9d83bb80730f40d6737ab7bd605" title="Click to view the MathML source">z₀class="mathContainer hidden">class="mathCode">$z_0$ 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.