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In this paper, we propose an equivariant degree based method to studybifurcation of periodic solutions (of constant period) in symmetric networks ofreversible FDEs. Such a bifurcation occurs when eigenvalues of linearizationmove along the imaginary axis (without change of stability of the trivialsolution and possibly without $1:k$ resonance). Physical examples motivatingconsidered settings are related to stationary solutions to PDEs with non-localinteraction: reversible mixed delay differential equations (MDDEs) andintegro-differential equations (IDEs). In the case of $S_4$-symmetric networksof MDDEs and IDEs, we present exact computations of full equivariantbifurcation invariants. Algorithms and computational procedures used in thispaper are also included.

Bifurcation of space periodic solutions in symmetric reversible FDEs