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Crandall, M.G. and Rabinowitz, P.H. (1977) The Hopf Bifurcation Theorem in Infinite Dimensions. Archive for Rational Mechanics and Analysis, 67, 53-72.
https://doi.org/10.1007/bf00280827

has been cited by the following article:

• TITLE: Dynamic Analysis of an HTLV-I Infection Model Involving CTL Immune Responses and Immunotaxis

  AUTHORS: Hongyan Kang, Yinji Huang

  KEYWORDS: Immune Chemotaxis, Hopf Bifurcation, Periodic Solutions, Stability

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.14 No.8, August 25, 2026

  ABSTRACT: This paper investigates the Hopf bifurcation problem for a class of reaction-diffusion models of HTLV-I infection that incorporate CTL immune responses and immunochemotaxis. Using the chemotaxis coefficient as the bifurcation parameter, this paper derives the conditions for the existence of a Hopf bifurcation at a positive equilibrium point and the existence of periodic solutions. Furthermore, it determines the bifurcation direction and stability of the periodic solutions: if ξ k 0 H ″ ( 0 )>0 , the bifurcation direction is supercritical, and the periodic solution is stable; if ξ k 0 H ″ ( 0 )<0 , the bifurcation direction is subcritical, and the periodic solution is unstable.