Differential and Integral Equations

Bifurcation of Space Periodic Solutions in Symmetric Reversible FDEs

Zalman Balanov and Hao-Pin Wu

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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

Permanent link to this document
https://projecteuclid.org/euclid.die/1487386827

Mathematical Reviews number (MathSciNet)
MR3611503

Zentralblatt MATH identifier
06738552

Subjects
Primary: 37G40: Symmetries, equivariant bifurcation theory 34k18 34k13 46N20: Applications to differential and integral equations 55M25: Degree, winding number 47H11: Degree theory [See also 55M25, 58C30]

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


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