Abstract
In this paper, we investigate the spatiotemporal pattern formation in a diffusive intraguild predation (IGP) model with a nonlocal interaction term in the growth of the shared resource, which extends previous studies of local reaction-diffusion IGP model. We first perform the stability and Hopf bifurcation analyses for the unique positive equilibrium of the corresponding non-spatial system, and give analytical formulas to determine the direction and stability of the bifurcating periodic solutions. Then the linear stability analysis for the nonlocal model shows that the nonlocal interaction is a key mechanism for the formation of Turing patterns. Numerical simulations show that low conversion rate from resource to IG predator can induce stationary Turing patterns, intermediate conversion rate can induce regular oscillatory patterns, and high conversion rate can induce irregular spatiotemporal chaotic patterns for certain diffusive rate. The impact of nonlocal interaction on the resulting patterns with certain diffusive rate is further explored by numerical simulations, which show that nonlocal interaction can induce pattern transition from stationary Turing patterns to non-stationary oscillatory patterns, and even to spatiotemporal chaotic patterns with the increase of the nonlocal interaction tensity. In addition, spatiotemporal chaotic patterns are found in the Turing-Hopf parametric space, which enrich pattern dynamics for diffusive IGP models with nonlocal interactions.
Highlights
Predation is one of the basic interspecies relationships in biology and ecology
Substituting it into (22) yields Re(λ′(βH1 )) = 0.0327, which indicates that the transversality condition holds. It follows from Theorem II.3 that E∗ will lose its stability and Hopf bifurcation occurs when β1 passes through its critical value βH1, that is, a family of periodic solutions bifurcates from the positive equilibrium E∗
We investigated pattern formation in a diffusive intraguild predation model with nonlocal interactions in the growth of the shared resource
Summary
Predation is one of the basic interspecies relationships in biology and ecology (see, for example, Murray). Banerjee et al. explored the effect of nonlocal interactions on spatiotemporal pattern formation including stationary patterns and non-stationary patterns as well as pattern transition from one type to another in several prey-predator models. All of these works just focused on two species, which raises a question of how to apply these results to multiple species models. Motivated by the above discussions, in this paper, we consider the following diffusive three species intraguild predation model with the nonlocal intra-specific competition for the shared resource:. The paper ends with a brief summary of our findings
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