Bifurcations in a Plant-Pollinator Model with Multiple Delays

The plant-pollinator model is a common widely researched by scholars in population dynamics. In fact, its complex dynamical behaviors are universally and simply expressed as class of delay differential-difference equations. this paper, based on several early models, we consider with two combined delays to further describe the mutual constraints between populations under different time qualitatively analyze stability Hopf bifurcation. Specifically, selecting combinations branch parameters analyzing detail distribution roots corresponding characteristic transcendental equation, investigate local positive equilibrium point equations, derive sufficient conditions asymptotic stability, demonstrate bifurcation for system. Under condition that not equal, some explicit formulas determining direction periodic solutions obtained differential equations using theory norm form theorem center manifold. end, examples presented computer numerical simulations taken support effectiveness our theoretical predictions.