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March/April 2017 Bifurcation of Space Periodic Solutions in Symmetric Reversible FDEs
Zalman Balanov, Hao-Pin Wu
Differential Integral Equations 30(3/4): 289-328 (March/April 2017).

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.

Citation

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Zalman Balanov. Hao-Pin Wu. "Bifurcation of Space Periodic Solutions in Symmetric Reversible FDEs." Differential Integral Equations 30 (3/4) 289 - 328, March/April 2017.

Information

Published: March/April 2017
First available in Project Euclid: 18 February 2017

zbMATH: 06738552
MathSciNet: MR3611503

Subjects:
Primary: 34K13, 34K18, 37G40, 46N20, 47H11, 55M25

Rights: Copyright © 2017 Khayyam Publishing, Inc.

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Vol.30 • No. 3/4 • March/April 2017
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