Predator-prey dynamics with personality-dependent foraging and maturation delay: stability switches, Hopf and Bogdanov-Takens bifurcations

Individual differences in predator boldness can alter encounter and attack rates, while maturation introduces biologically realistic time lags. We couple these two mechanisms in a Rosenzweig-MacArthur framework by modeling a nonlinear, personality-dependent attack rate and deriving a stage-structured maturation delay for predators, yielding a delay differential equation system. For the delay-free model, we establish positivity and boundedness, characterize boundary and interior equilibria, and provide a complete local bifurcation picture: transcritical and saddle-node bifurcations together with Hopf bifurcations that generate stable cycles; at codimension two, we prove the occurrence of cusp/Bogdanov-Takens points with accompanying homoclinic loops. Introducing maturation delay produces delay-induced complexity: multiple stability switches, sequences of Hopf bifurcations on distinct frequency branches, and global Hopf continua that connect critical delays. Analytical predictions are corroborated numerically via continuation (DDE-BIFTOOL), revealing periodic and quasi-periodic oscillations as well as bistability between coexistence and boundary states. Our results identify personality heterogeneity and developmental timing as interacting drivers of oscillatory and multistable dynamics, and provide parameter thresholds, expressed in biologically interpretable combinations, for when coexistence equilibria lose or regain stability. These findings refine theory for delayed predator-prey interactions and suggest targets (e.g., handling/harvest and juvenile survival) for stabilizing management in systems with behavioral variation.