Study Of Predator-Prey Models With Different Predators' Hunting Stategies

In our paper,we have applied various predator-prey models to case studies with different predators' hunting strategies,including hunting prey by individual,cooperation with others or both of the two above strategies.To solve these problems,we construct mathematical models and simulation models considering densities of predators and prey evolving through time,the spatial distribution and so on.Each method has its own limitations;therefore we should combine these methods to solve the issues.The structure of the paper is as follows.The first section gives a brief introduction to the research background and current research status of the predator-prey model.In the second section,we construct two models which predators hunting by itself.First,predators and prey have their own range of visions respectively.Predators chasing their prey based on their visions,and prey escape from predators based on their visions.Using the Monte Carlo simulations,we know that the predators with larger visions and the prey with lower visions can survive in the system easily.However,the price of evolution is the lower numbers of their populations.That is to say,only the reasonable evolution is beneficial.Then we discuss the emergence of predators who never hunt by themselves.It turned out that the emergence of the "lazy" predators is beneficial for the systems sometimes.In the third section,predators can hunt their prey cooperating with other predators in their group.In this model,the new-born predator can stay in the same group with its parent or build a new group.We can krnow from the results after using the mean-field method and Monte Carlo simulation that the distributions of the group size of predators are as same as previous observations.That is to say,the probability of the new-born predator stay in the same group with its parent is significant.In the last section,we shovw a predator-prey model which predators can change their hunting strategies when they met different prey.Prey are aged into the adult prey and the juvenile prey.The juvenile prey can grow into the adults,and the adults reproduce the juveniles.Predators catch the adult prey in groups and catch the juvenile prey by itself.We find that the group prey of predators has little influence on the system and the prey with higher grow rates are more competitive most times.To sum up,the study of predator-prey systems is important and necessary;the results are real and helpful.