Hopf bifurcation analysis in a diffusive predator-prey model with repulsive predator-taxis and digestion delay

In this paper, we investigate the joint effect of repulsive predator -taxis and digestion delay in a diffusive predator-prey model. Our theoretical findings reveal that, when both species exhibit logistic growth, the predator -taxis does not lead to Turing bifurcation. However, the introduction of digestion delay gives rise to the occurrence of spatially homogeneous and inhomogeneous Hopf bifurcations which result in spatially homogeneous and inhomogeneous periodic solutions. In particular, the inhomogeneous Hopf bifurcations are often accompanied by rich and diverse pattern modes. Under certain conditions, the spatially homogeneous Hopf bifurcation disappears, while the spatially inhomogeneous Hopf bifurcations persist. Furthermore, our analysis reveals the existence of double Hopf bifurcation between homogeneous and inhomogeneous states in the bifurcation diagram. Finally, the numerical simulations confirm the theoretical findings and demonstrate the emergence of various spatial patterns with different values of predator -taxis coefficients and delays. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.