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Equivariant normal forms for neutral functional differential equations

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Abstract

This paper addresses the computation of equivariant normal forms for some Neutral Functional Differential Equations (NFDEs) near equilibria in the presence of symmetry. The analysis is based on the theory previously developed for autonomous retarded Functional Differential Equations (FDEs) and on the existence of center (or other invariant) manifolds. We illustrate our general results by some applications to a detailed case study of additive neurons with delayed feedback.

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Authors and Affiliations

  1. College of Mathematics and Econometrics, Hunan University, Changsha, Hunan, 410082, People’s Republic of China

    Shangjiang Guo

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  1. Shangjiang Guo
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Correspondence to Shangjiang Guo.

Additional information

This work was partially supported by NNSF of China (Grant No. 10971057), by the SRF for ROCS and the Key Project (Grant No. [2008]890 & [2009]41) of SEM, and by Scientific Research Fund of Hunan Provincial Education Department.

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Guo, S. Equivariant normal forms for neutral functional differential equations. Nonlinear Dyn 61, 311–329 (2010). https://doi.org/10.1007/s11071-009-9651-4

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  • DOI: https://doi.org/10.1007/s11071-009-9651-4

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