Global Bifurcation of Periodic Solutions in Symmetric Reversible Second Order Systems with Delays

被引：6
作者：
Balanov, Zalman [1 ,2 ]
Burnett, Joseph [2 ]
Krawcewicz, Wieslaw [1 ,3 ]
Xiao, Huafeng [1 ,3 ]
机构：
[1] Xiangnan Univ, Dept Math, Chenzhou 423000, Hunan, Peoples R China
[2] Univ Texas Dallas, Dept Math Sci, Richardson, TX 75080 USA
[3] Guangzhou Univ, Appl Math Ctr, Guangzhou 510006, Guangdong, Peoples R China
来源：
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2021年 / 31卷 / 12期
基金：
中国国家自然科学基金;
关键词：
Second order system; delay-differential equation; autonomous system; periodic solution; commensurate delay; Brouwer equivariant degree; Burnside ring; reversible system; global bifurcation; BOUNDARY-VALUE-PROBLEMS; DIFFERENTIAL-EQUATIONS; MULTIPLE SOLUTIONS; EXISTENCE;
D O I：
10.1142/S0218127421501807
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Global bifurcation and spatio-temporal patterns of periodic solutions (with prescribed period) to second order reversible equivariant autonomous systems with commensurate delays are studied using the Brouwer/Leray-Schauder O(2) x Gamma x Z(2)- equivariant degree theory. Here, O(2) is related to the reversal symmetry combined with the autonomous form of the system, Gamma reflects extra spacial symmetries of the system, and Z(2) is related to the oddness of the right-hand side. Abstract results are supported by a concrete example with Gamma = D-6 - the dihedral group of order 12.
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页数：23
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