Normal forms and Hopf bifurcation for partial differential equations with delays

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Delay Differential Equations and Applications (2006, background): “Details and examples of applications can be found in [37].”
Turing Instability and Turing–Hopf Bifurcation in Diffusive Schnakenberg Systems with Gene Expression Time Delay (2018, methodology): “Within the framework of Faria [5,6], Jiang et al. [14] gave explicitly generic formulas for calculating coefficients of normal forms up to order 3 for codimension-two Hopf-steady state bifurcation of delayed reaction-diffusion equations with Neumann boundary conditions, which include TuringHopf bifu”
Formulation of the normal form of Turing-Hopf bifurcation in partial functional differential equations (2020, methodology): “We follow the framework of Faria [15,17] to reduce the general PFDEs with perturbation parameters to three-dimensional systems of ODEs up to third order, restricted on the local center manifold near a Hopf-steady state type of singularity, and the unfolding parameters can be expressed by those origi”
Hopf bifurcation in a delayed reaction-diffusion-advection population model (2017, background): “For models with the homogeneous Neumann boundary conditions, researchers were mainly concerned with the Hopf bifurcation near the constant positive equilibrium, see [9, 13, 15, 18, 19, 22, 26, 28, 31, 32] and the references therein.”