Abstract: This thesis investigates the dynamics of a host–parasite–competitor model with biologically motivated time delays. By incorporating a parasite maturation delay, the delayed system exhibits dynamical behaviours that are absent in the corresponding ordinary differential equation model.

Using linear stability and bifurcation analysis, conditions for Hopf, generalized Hopf (Bautin), and Hopf–zero bifurcations are established, providing analytical criteria for the stability and local bifurcation structure of the delayed system. Numerical simulations, together with bifurcation diagrams, Lyapunov exponent estimates, and return maps, are used to investigate the post-Hopf dynamics of the delayed system.

Overall, this thesis presents a theoretical and numerical investigation of delay-induced dynamics in host–parasite–competitor systems. The results demonstrate how biologically motivated time delays influence the stability and bifurcation structure of the model, providing new insights into the dynamics of ecological systems with delayed interactions.