## Differential and Integral Equations

### Bifurcation of Space Periodic Solutions in Symmetric Reversible FDEs

#### Abstract

In this paper, we propose an equivariant degree based method to study bifurcation of periodic solutions (of constant period) in symmetric networks of reversible FDEs. Such a bifurcation occurs when eigenvalues of linearization move along the imaginary axis (without change of stability of the trivial solution and possibly without $1:k$ resonance). Physical examples motivating considered settings are related to stationary solutions to PDEs with non-local interaction: reversible mixed delay differential equations (MDDEs) and integro-differential equations (IDEs). In the case of $S_4$-symmetric networks of MDDEs and IDEs, we present exact computations of full equivariant bifurcation invariants. Algorithms and computational procedures used in this paper are also included.

#### Article information

Source
Differential Integral Equations, Volume 30, Number 3/4 (2017), 289-328.

Dates
First available in Project Euclid: 18 February 2017

https://projecteuclid.org/euclid.die/1487386827

Mathematical Reviews number (MathSciNet)
MR3611503

Zentralblatt MATH identifier
06738552

#### Citation

Balanov, Zalman; Wu, Hao-Pin. Bifurcation of Space Periodic Solutions in Symmetric Reversible FDEs. Differential Integral Equations 30 (2017), no. 3/4, 289--328. https://projecteuclid.org/euclid.die/1487386827