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Global Hopf bifurcations of neutral functional differential equations with state-dependent delay

  • * Corresponding author: Xiuli Sun

    * Corresponding author: Xiuli Sun 

The second author is supported by NSFC grant No.11371058 and the Fundament Research Funds for the Central University. The third author is supported by NSFC grant No.11501409

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  • A global Hopf bifurcation theory for a system of neutral functional differential equations (NFDEs) with state-dependent delay is investigated by applying the $S^{1}$-equivariant degree theory. We use the information about the characteristic equation of the formal linearization with frozen delay to detect the local Hopf bifurcation and to describe the global continuation of periodic solutions for such a system. The results are important in studying bifurcations of NFDEs with state-dependent delay.

    Mathematics Subject Classification: Primary: 34K18, 34K20; Secondary: 34C23, 34C25, 37G10, 37G15.


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