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Based on biological meaning, a kind of diffusive intraguild predation (IGP: resource, IG prey and IG predator) model with delay effect is investigated in this paper. The model has Holling-Type I functional response between resource-IG prey and resource-IG predator; Holling-Type II functional response between IG prey and IG predator. We first give sufficient conditions on the stability of possible nonnegative constant steady-state solutions for the proposed model, which give us a complete picture of the global dynamics. Then we investigate Hopf bifurcation near the unique positive constant steady-state solution by taking delay as bifurcation parameter and derive the Hopf bifurcation threshold. It is shown that the delay can induce three types of bistability (node-node bistability, node-cycle bistability and cycle-cycle bistability), periodic oscillations and irregular oscillations triggering spatiotemporal chaos in the diffusive IGP model. Numerical simulations are performed to illustrate our theoretical results and suggest that delay can even trigger the emergence of self-organised spatiotemporal patterns, which evolve from spiral patterns to irregular spatial patterns via spatiotemporal Hopf bifurcation. In addition, the impact of diffusion on the model’s dynamics under certain time delay are also explored. [ABSTRACT FROM AUTHOR]

The nonlinear incidence rate can explain the complicated infectious process of disease. And time delay describing the latent period widely exists in the process of disease contagion. In this paper, a spatiotemporal epidemic model with nonlinear incidence rate is investigated. In particular, we considered that the time delay is relatively small. In this case, the characteristic equation are derived, we obtain two mechanisms of instability of the positive constant stationary state, that is, One is the diffusion induced instability, and the other one is delay induced instability. Moreover, the results of numerical simulation validate our theoretical analyses. The obtained results may well catch some major features for epidemic models. [ABSTRACT FROM AUTHOR]