Spatiotemporal pattern formation in a pollen tube model with nonlocal effect and time delay

Abstract

The dynamics of a pollen tube model with nonlocal effect and time delay is investigated in this paper. Compared with the model without delay, a double Hopf bifurcation due to the interaction of homogeneous and nonhomogeneous Hopf bifurcations can occur and quasi periodic patterns can be observed. Besides, the interaction of Turing bifurcation and spatially nonhomogeneous Hopf bifurcation will lead to some new spatiotemporal patterns. • Influence of delay and nonlocal effect on the spatiotemporal dynamics of a pollen model is investigated. • Delay-induced Hopf bifurcation at the first critical value could be homogeneous or nonhomogeneous. • The interaction of spatially homogeneous and nonhomogeneous Hopf bifurcation will lead to co-dimension 2 double Hopf bifurcation. • The interaction of spatially nonhomogeneous Hopf bifurcation and Turing bifurcation can lead to co-dimension 2 Turing–Hopf bifurcation.