Dynamics Of A Predator-prey Metapopulation With Prey Toxin Effects

Because of many kinds of predation phenomenon, every individual may be prey in nature, but the natural balance can be seen everywhere. With the high pressure of predator, the prey have to adjust themselves to meet the environment and withstand the every kinds of natural enemy in the process of survival and evolution. Prey can produce some toxic components, in addition, these toxic components be call prey toxin traditionally, which can cause some special damage to the predator. Prey toxins are the most effective defensive weapon, when the prey is touched when or eaten, the toxin will play a role.In recent years, theoretical ecologists and field ecologists carried out a lot of theory and practice to study the influence of prey protection of biological toxins, invasive species ecology and population dynamics phenomena. Of course, study toxins become prey ecology, invasion biology and one of the hotspots of Conservation Biology. About the impact on the level of metapopulation prey toxin on the predation,whether theoretical or experimental studies are very scarce. Predation may significantly affect the distribution and species distribution patterns. Therefore, the study of the impact of prey toxins on the relationship of predator system is significant at the level of metapopulation. By establishing predator system has the role of toxins in the metapopulation theory model, with the mathematical analysis,numerical simulation and phase plane analysis method to study the predation system with toxins like metapopulation model and Allee effect on predation system with toxic effects affect metapopulation model.In this paper, we chose a typical predator-prey metapopulation system, based on the assumption that prey can produce toxins, and build a new predator-prey metapopulation system.In the next moment, we discussed the impact of prey toxin on the Allee-like effects prey metapopulation. Through analysis and simulation, we learned that due to the prey toxins, with the scope of the appropriate parameters, system is easier to reach the equilibrium state. What is more, because of this system contains of prey Allee-like effects, it has a bistable state and a saddle-node bifurcation. Under the action of prey toxins, the proportion of the prey in the equilibrium state increases, and the proportion of the predator in the equilibrium state decreases.