In this paper, we delve into double Hopf bifurcation induced by memory-driven directed
movement in a spatial predator-prey model with Allee effect and maturation delay of preda-
tors. We first adopt a novel technique to handle the associated characteristic equation and
thus obtain the crossing curves as well as the double Hopf points. We then calculate explicit
formulae of normal form regarding non-resonant double Hopf bifurcation. We thus divide
the dynamics of the developed model into several categories near the double Hopf bifurcation
points. Our numerical and theoretical results both demonstrate that the model can exhib-
it various complex phenomena when the parameters are near the double Hopf bifurcation
points. For example, the transition from one stable spatially inhomogeneous periodic orbit
with mode-5 to another with mode-4 and the coexistence of them can be observed.
（S. Li, S. Yuan, Z. Jin et al., Double Hopf bifurcation induced by spatial
memory in a diffusive predator–prey model with Allee effect and maturation delay of predator.
Communications in Nonlinear Science and Numerical Simulation (2024), doi:
https://doi.org/10.1016/j.cnsns.2024.107936.）