Local Hopf bifurcation analysis of logistic population dynamics models with two delays

Multiple time lags can occur very naturally in the study of population dynamics. In this paper, we study two forms of the delay logistic equation with two discrete time delays. For both the models, we identify the condition for the first local Hopf bifurcation. For our analysis, we employ a non-dimensional bifurcation parameter. Using Poincaré normal forms and the center manifold theory, we also conduct the requisite analysis to determine the type of the Hopf bifurcation. This enables us to determine the asymptotic orbital stability of the bifurcating periodic solutions. The analysis is complemented with some numerical examples and bifurcation diagrams.