Pattern dynamics of a predator–prey reaction–diffusion model with spatiotemporal delay
Using the tool of Turing instability for partial differential equations, we investigate the spatiotemporal distributions for solutions of a predator–prey-type reaction–diffusion model with spatiotemporal delay. The linear stability conditions of Turing instability, which induce bifurcation patterns in this model, are obtained. Moreover, according to these conditions, we numerically calculate the bifurcation diagrams by using time delay and the predator rate as parameters. The effects of two parameters in the different bifurcation diagrams are also demonstrated through numerical computations and lead to some spatiotemporal patterns of this model, which enrich the pattern formation of predator–prey models.
KeywordsPredator–prey model Spatiotemporal patterns Turing instability Spatiotemporal delay
The authors thank the anonymous referees for their valuable comments on improvement of the presentation of this work. This work is supported by the State Key Program of National Natural Science Foundation of China under Grant No.11032009 and National Natural Science Foundation of China under Grant No.11272236.
Conflict of interest
The authors declare that the work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
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