Periodic Solutions to Reversible Second Order Autonomous Systems with Commensurate Delays

2020/07/16 by Balanov, Zalman, Chen, Fulai, Guo, Jing +1 · 1 citation
#Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2007.09166

Abstract

Existence and spatio-temporal patterns of periodic solutions to second order reversible equivariant autonomous systems with commensurate delays are studied using the Brouwer O(2) × Γ× \mathbb Z₂-equivariant degree theory, where O(2) is related to the reversing symmetry, Γ reflects the symmetric character of the coupling in the corresponding network and \mathbb Z₂ is related to the oddness of the right-hand-side. Abstract results are supported by a concrete example with Γ= D₆ -- the dihedral group of order 12.

Cited by

• Unbounded Branches of Non-Radial Solutions to Semilinear Elliptic Systems on a Unit Ball in \mathbb R³ and Their Patterns

Related

• Periodic Solutions to Reversible Second Order Autonomous DDEs in\n Prescribed Symmetric Nonconvex Domains
• Existence and Spatio-Temporal Patterns of Periodic Solutions to Second Order Non-Autonomous Equivariant Delayed Systems
• Patterns of Non-Stationary Solutions to Symmetric Systems of Second-Order Differential Equations
• Bifurcation of space periodic solutions in symmetric reversible FDEs
• Subharmonic Solutions In Reversible Non-Autonomous Differential Equations