A study of the turing pattern formation in a predator-prey model based on network and non-network environments

In this work, we have established the predator-prey model with time delay based on network and non-network environments. We study the Turing instability of this model in continuous and discrete media respectively. Based on the conditions for the Turing instability, we carry out a lot of numerical simulations for the ordinary model and the network version model respectively, and analyze the influence of the diffusion coefficients and other parameters on the pattern structure. From this we can see that the model in continuous media and discrete media usually have the same pattern structure when it is finally stabilized, but the time required for pattern stabilization in these two cases is different, and it usually takes more time when there is in the case of non-network. And the parameters in the model would have a certain impact on the pattern formation. The conclusion we obtained is helpful to maintain the balanced development of biological populations and protect the diversity of biological species.